how to pass external .css into jsp? (path issue)
Accessing Resources from JSP inside WEB-INF
If $(X_n)$ is i.i.d. and $ \frac1n\sum\limits_{k=1}^{n} {X_k}\to Y$ almost surely then $X_1$ is integrable (converse of SLLN) Let $(\Omega,\mathcal F,P)$ be a finite measure space.  Let $X_n:\Omega \rightarrow \mathbb R$ be a sequence of iid r.v's  I need to prove that if:  $ n^{-1}\sum _{k=1}^{n} {X_k} $ converges almost surely to $Y$ then all $X_k$ have expectation.  If I understand correctly then $X_k$ has expectations means $X_k$ is in $\mathcal L^1(\Omega)$.  And I know that on finite measure space Converging in expectations is converging in $\mathcal L^1(\Omega)$ and it's stronger than almost sure convergence.  And I know that from linearity of expectation even if one of the sequence is not in $\mathcal L^1(\Omega)$ then $Y$ is not in $\mathcal L^1(\Omega)$.  How do I continue? Posting and answering questions you have already found the answer to Is there a correct gender-neutral singular pronoun ("his" vs. "her" vs. "their")? Is there a pronoun I can use as a gender-neutral pronoun when referring back to a singular noun phrase?  Each student should save his questions until the end. Each student should save her questions until the end. How to generate world files for raster X? How to ignore the first line of data when processing CSV data? Windows 7 low and critical battery levels cannot be set lower than 10% Definitions of "linearity" across branches of mathematics or levels of math education Linearity is a ubiquitous concept in mathematics; however, each branch of mathematics appears to have its own definition of what a linear map (function, functional, functor, transformation, form, operator, or whatsoever) is. These different definitions can lead to confusion, especially when people apply conflicting definitions of linearity to the same mathematical object (just  to figure out what I mean).  One of my favorite examples with potential for conflict is the natural logarithm $\ln : \mathbb{R}_{&gt;0} \to \mathbb{R}$, which the majority of people, as I could learn during hot disputations not only  but also with colleagues in my field, regard as clearly non-linear, even though it fully complies with the definition of a linear map from the vector space $\mathbb{R}_{&gt;0}$ to the vector space $\mathbb{R}$ (cf. Definition 4 below). A similar conflict arises analogously for the exponential function $\exp :\mathbb{R} \to \mathbb{R}_{&gt;0}$.  I do not want to initiate yet another discussion here, about what the right and what the wrong definition of linearity is! Rather, ...  ... I would like to compile a list of existing definitions, to get a better overview of the different uses of the term "linearity" across the different branches of mathematics and levels of education.    Let be begin with the following four, which are certainly far from constituting a complete list. What about bilinear or multilinear forms, linear morphisms and linear functors in category theory, linear metrics, or other concepts of linearity? I am looking forward to see your answers.  At school I was taught that     Definition 1:   A function $f$ is linear if it is of the form $f(x) = ax + b$.   Later I learned that $f(x) = ax + b$ is affine, rather than linear, because     Definition 2:   A function $f$ is linear if it is of the form $f(x) = ax$.   From real analysis and systems theory, I know the following     Definition 3:   A map $f$ is linear if         $f(x + y) = f(x) + f(y)$   $f(a \cdot x) = a \cdot f(x)$.      This definition also applies to the expected value in statistics, as        $\mathrm{E}(X + Y) = \mathrm{E}(X) + \mathrm{E}(Y)$   $\mathrm{E}(a \cdot X) = a \cdot \mathrm{E}(X)$.      In a linear algebra course, I learned for the first time that we must not forget to take into account that the vector-space operations of the domain and the codomain of a map $f$ may be dissimilar. In fact, if $(V, \oplus, \odot)$ and $(W, \boxplus, \boxdot)$ are two $\mathbb{K}$-vector spaces, then     Definition 4:   A map $f : V \to W$ is linear if         $f(x \oplus y) = f(x) \boxplus f(y)$   $f(a \odot x) = a \boxdot f(x)$.         Notice that I deliberately used distinct symbols for the operations in both vector spaces, to emphasize how this definition differs from Definition 3.   Correct me if I am wrong, but this definition should also apply to maps between two modules.    Updates: Why light moves sideways? Greatings!  I'm trying to understand special relativity and have one question bugging me.  In almost every book or video about the subject there is a thought experiment with moving light clock. I hope I need not elaborate on the sutup and the outcome of the experiment.  So the question is this: When a light source on the MOVING light clock emits a photon of light the path of the photon is triangular.   How this can be?   I thought since light speed is constant in every reference frame the movment of the "emmiter" can't affect the movment of the light so light should shoot right up (from the point of stationary observer) and thus move backward and up from the point of moving observer.  So you see my logic is: light speed is invariant => you can't make it move UP &amp; FORWARD only UP. i.e. you can't change it's direction once it's emited in UP direction. Why the hell light moves sideways then?  And I'm puzzeled. There is flaw in the logic but I don't see it.  Thanks for help. Thought Experiment - Poking a stick across a Black Hole's Event Horizon Is there any function that converts an escaped Url string to its unescaped form? System.Web.HttpUtility.UrlDecode() can do that job but I don't want to add a reference to System.Web.dll. Since my app is not a web application, I don't want to add a dependency for only using a function in an assembly.  UPDATE: Check  about the same issue. When is $f=\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^5-3x+\ln5$ decreasing $\forall\; x$? When is $$f=\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^5-3x+\ln5$$ decreasing $\forall\; x$?    Diffrentiating: $$f'=5\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^4-3$$ If $f$ is decreasing, $f'&lt;0$: $$5\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^4-3&lt;0\implies x^4&lt;\frac3{5\left(\frac{\sqrt{p+4}}{1-p}-1\right)}$$ Since if $\left(\frac{\sqrt{p+4}}{1-p}-1\right)\to0^+\implies x^4&lt;+\infty$, which holds forallx, So:$$p=\frac{3\pm\sqrt{21}}2$$which doesn't ply with textbook-answer, since it mentions an domain for p. Is it "re-offend" or "reoffend"? I want to know whether there is a hyphen in the word re-offend, or if it is spelt reoffend. I looked in Oxford English dictionary and the word "reoffend" appears, but then I checked Merriam-Webster and the word is not in there.  So is reoffend a word or is it re-offend?  I'm in Australia where we observe UK English if that matters. I was given the files for a mini linux, that boots directly into firefox. It works for all it should be doing, only that I do not get an internet connection.  We have 3 DNS servers in the network, which all work. I can ping them, too. But when trying to ping google.de or wget google.de I get a bad address error.  nslookup google.de works for some reason.  I tracked the issue down to my resolv.conf on the booted system not having the same contents as the resolv.conf that I put into the .iso file.  I tried understanding all the factors that go into creating and modifying resolv.conf. I'm not quite sure I got it all, but I definitely didn't find my solution there.  So as a last ditch effort, I tried making the resolv.conf file immutable using   :~# chattr +i /etc/resolv.conf   When rebuilding and booting again to my surprise my file was renamed to resolv.conf~ and in its place was the same standard file that has been haunting me.   The file contents make me believe it gets the information from the network itself. When starting the .iso in Virtualbox without internet access, my file is being kept as it is.  I tried changing /etc/dhcp/dhclient.conf to not get the information from the net, by deleting domain-name-server and domain-name-search from the request part of the file.  Didn't work unfortunately.  I don't have the NetworkManager installed. The iso is based on Ubuntu 14.04.  There is probably vital information missing. I'm happy to provide it.  UPDATE:  I think I found the file that clears resolv.conf.  It seems to be /usr/share/udhcpc/default.script  #!/bin/sh  # udhcpc script edited by Tim Riker &lt;Tim@Rikers.org&gt;  [ -z "$1" ] &amp;&amp; echo "Error: should be called from udhcpc" &amp;&amp; exit 1  RESOLV_CONF="/etc/resolv.conf" [ - n "$broadcast" ] &amp;&amp; BROADCAST="broadcast $broadcast" [ -n "$subnet" ] &amp;&amp; NETMASK="netmask $subnet"  case "$1" in     deconfig)         /bin/ifconfig $interface 0.0.0.0         for i in /etc/ipdown.d/*; do             [ -e $i ] &amp;&amp; . $i $interface         done         ;;      renew|bound)         /bin/ifconfig $interface $ip $BROADCAST $NETMASK          if [ -n "$router" ] ; then             echo "deleting routers"             while route del default gw 0.0.0.0 dev $interface ; do                 :             done              metric=0             for i in $router ; do                 route add default gw $i dev $interface metric $((metric++))             done         fi          echo -n &gt; $RESOLV_CONF # Start ----------------           [ -n "$domain" ] &amp;&amp; echo search $domain &gt;&gt; $RESOLV_CONF         for i in $dns ; do             echo adding dns $i             echo nameserver $i &gt;&gt; $RESOLV_CONF         done         for i in /etc/ipup.d/*; do             [ -e $i ] &amp;&amp; . $i $interface $ip $dns          done # End ------------------         ;; esac  exit 0   It's part of the udhcpc program. A tiny dhcp client, that is part of busybox  Will investigate further.    UPDATE2 AND SOLUTION:  I commented the part out (#Start to #End), that seemingly overwrites the /etc/resolv.conf file and sure enough. That was the culprit. So an obscure script caused all this trouble.  I changed the question to reflect, what actually needed to be known to solve my problem, so it would be easier to find for people with the same problem and so I could accept an answer.  Thanks for the help here in figuring things out. I have the following query that sort of works, but I find it to be kludgy and inefficient.  Is there a better way to write this query?  I know this is a bit of an odd query, else I would probably have found some advice when searching, but it is necessary for our business logic.  We've been doing this in Hibernate queries and using software to output the file but we're needing to improve performance drastically and that means using raw sql.  The output of this query is to be used to partially populate a helper table that we query to figure out which of our 40-odd product tables a particular item is contained in.  Could the following query be replicated using something like GROUP_CONCAT in reverse? Note that the second and third column must be repeated on each line.  The fields all contain the same type of data.  SELECT 'Pn', 'Mfg', 'TableId', 'SourceColumn', 'OtherData' SELECT PN1, Mfg, '26', 'PN1', OtherData FROM Table  UNION ALL SELECT PN2, Mfg, '26', 'PN2', OtherData FROM Table UNION ALL SELECT PN3, Mfg, '26', 'PN3', OtherData FROM Table UNION ALL SELECT PN4, Mfg, '26', 'PN4', OtherData  INTO OUTFILE 'XXX.dat' FIELDS TERMINATED BY ',' OPTIONALLY ENCLOSED BY '"' ESCAPED BY '\\' LINES TERMINATED BY '\n' FROM Table d;   Input looks like the following table:       |  PN1  |  PN2  |  PN3    |  PN4    |  MFG  |  TableId  |  OtherData  |     -----------------------------------------------------------------------     |  asdf |  abde |  12354  |  asdfc  |  2    |  26       |  0.2456     |     |  nupo |  1354 |  null   |  null   |  2    |  26       |  1.53       |     |  ...  |  ...  |  ...    |  ...    |  ...  |  ...      |  ...        |     |  ...  |  ...  |  ...    |  ...    |  ...  |  ...      |  ...        |     |  ...  |  ...  |  ...    |  ...    |  ...  |  ...      |  ...        |   I want the output .dat file to look like this:       "Pn","Mfg","TableId","SourceColumn","OtherData"     "asdf",2,26,"PN1",0.2456     "abde",2,26,"PN2",0.2456     "12354",2,26,"PN3",0.2456     "asdfc",2,26,"PN4",0.2456     "nupo",2,26,"PN1",1.53     "1354",2,26,"PN2",1.53     ...     ...     ...   If I take the INTO OUTFILE clause out, I get an output that looks like this:       |  Pn      |  Mfg     |  TableId    |  SourceColumn  | OtherData  |     -----------------------------------------------------------------     |  "Pn"    |  {blob}  |  "TableId"  |  "PN"          |  {blob}    |     |  "asdf"  |  {blob}  |  "PN1"      |  "PN1"         |  {blob}    |     |  "abde"  |  {blob}  |  "PN2"      |  "PN2"         |  {blob}    |     |  "12354" |  {blob}  |  "PN3"      |  "PN3"         |  {blob}    |     |  "asdfc" |  {blob}  |  "PN4"      |  "PN4"         |  {blob}    |     |  "nupo"  |  {blob}  |  "PN1"      |  "PN1"         |  {blob}    |     |  "1354"  |  {blob}  |  "PN2"      |  "PN2"         |  {blob}    |     |  ...     |  ...     |  ...        |   ...          |   ...      |     |  ...     |  ...     |  ...        |   ...          |   ...      |     |  ...     |  ...     |  ...        |   ...          |   ...      | Does Python support short-circuiting? What is "#!' in a script file? $cat shebang.sed  #! /bin/sed -f s/red/xxx/ s/BLUE/1234/  $./shebang.sed rgb lower (#1): "xxx green blue" UPPER (#2): "RED GREEN 1234"  $sed -f shebang.sed rgb lower (#1): "xxx green blue" UPPER (#2): "RED GREEN 1234"   I may guess what #! is doing. However, I don't say I know it. what is "#!"? What does “a couple” mean to you, and what does “a few” mean to you? Where does "wicked" get its /ɪd/ from? There are three ways I know to pronounce the -ed at the end of an adjective:   /t/ as in cracked. /d/ as in lined. /ɪd/ as in naked   I realise naked is a special case because, as , it comes for Old English nacod, so the suffix isn't added.   shows the pattern of pronunciation of -ed in all other cases. However it doesn't explain why  ends with /ɪd/ (or /id/ or /əd/ depending on the dialect).   that wicked comes from OE wicca, so the d wasn't already there.  Why do we pronounce wicked as /ˈwɪkɪd/ and not /ˈwɪkt/? Deriving ordered statistics minimum cdf Assume ${{X}_{1}}$, ${{X}_{2}}$, ${{X}_{3}}$,...,${{X}_{n}}$  are i.i.d. samples from distribution with density f, and cdf F.  Let V=min( ${{X}_{1}}$, ${{X}_{2}}$, ${{X}_{3}}$,...,${{X}_{n}}$)  To find the minimum $${B}_{v}={\{V\ge{v}\}}=\{{X}_{1}\ge{v}\}\cap\{{X}_{2}\ge{v}\}\cap...\cap\{{X}_{n}\ge{v}\}$$  So, $$P(V\ge{v})=[1-F(v)]^{n}$$  The cdf is  $$F_{v}(V)=1-[1-F(v)]^{n}$$   The density is $${f}_{v}(V)=\frac{d}{dv}[1-F(v)]^{n}=nf(v)[1-F(v)]^{n-1}$$   To find the density, why did we use $[1-F(v)]^{n}$ instead of $1-[1-F(v)]^{n}$, shouldn't we used the cdf to derive the pdf? What's the difference between semicolon and double ampersand && What is the difference between  echo "Hello " ; echo "world"   and  echo "Hello " &amp;&amp; echo "world"   Both seems to run the two commands after each other.