Does it imply that $\int _0^\infty f_n\to \int _0^\infty f$? If $f_n$ is a sequence of continuous functions such that $f_n$ converges to $f$ uniformly . Does it imply that $\int _0^\infty f_n\to \int _0^\infty f$?  I think the answer is no though I could not find a counter-example. Because if $f_n\to f$ uniformly then $\int _0^\infty |f_n-  f|&lt;\epsilon \times \infty $ which is undefined.
Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$? If $\displaystyle\{f_n(x)\}$ is sequence of continuous function on $\mathbb{R}$ converging uniformly to $f(x)$, then does $\displaystyle\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x) dx\,$ hold? I know  it holds if we integrate over an interval of the form $[a,b]$ but not sure about improper integral!
Can I use Divine Intervention or Wish to regain Wish? After reading this question on , I started wondering if there are ways for them to regain that ability.  I figured a Divine Intervention is probably strong enough as that is a god's power, as well as a second caster casting wish to undo the first wish (and thereby undoing its effects).  Are these valid ways of regaining the ability to cast wish? I tried to find an answer to this a few years ago, but it seemed it wasn't possible then (I suspect it isn't now either! - but what the hell!)   I have a three monitor system, that I mostly use for remote desktop. However occasionally it would be useful to have remote desktop on two monitors and use the other monitor for the local machine.   I know it is possible to have a single monitor full screen, or to stretch an RDP session across monitors, but this loses things like snapping etc.   P.S. this is a duplicate of  thread, but that was a couple of years ago, I'm hoping things have changed. I have a HP Pavilion dm4-2070us which has an Intel Corporation Centrino Wireless-N 1000 adapter.   The problem is that my computer doesn't show the wireless networks after I upgraded my system to Ubuntu 11.10. Following is my output for sudo lshw -class network:  *-network DISABLED          description: Wireless interface    product: Centrino Wireless-N 1000    vendor: Intel Corporation    physical id: 0    bus info: pci@0000:01:00.0    logical name: wlan0    version: 00    serial: 8c:a9:82:81:5a:30    width: 64 bits    clock: 33MHz    capabilities: pm msi pciexpress bus_master cap_list ethernet physical wireless    configuration: broadcast=yes driver=iwlagn driverversion=3.0.0-12-generic firmware=39.31.5.1 build 35138 latency=0 link=no multicast=yes wireless=IEEE 802.11bgn    resources: irq:42 memory:c2500000-c2501fff  *-network    description: Ethernet interface    product: AR8151 v2.0 Gigabit Ethernet    vendor: Atheros Communications    physical id: 0    bus info: pci@0000:08:00.0    logical name: eth0    version: c0    serial: 2c:41:38:07:f3:e3    size: 100Mbit/s    capacity: 1Gbit/s    width: 64 bits    clock: 33MHz    capabilities: pm msi pciexpress vpd bus_master cap_list ethernet physical tp 10bt 10bt-fd 100bt 100bt-fd 1000bt-fd autonegotiation    configuration: autonegotiation=on broadcast=yes driver=atl1c driverversion=1.0.1.0-NAPI duplex=full firmware=N/A ip=192.168.1.7 latency=0 link=yes multicast=yes port=twisted pair speed=100Mbit/s    resources: irq:44 memory:c1400000-c143ffff ioport:2000(size=128)   The output for rfkill list all:  0: hp-wifi: Wireless LAN     Soft blocked: no     Hard blocked: no 1: hp-bluetooth: Bluetooth     Soft blocked: no     Hard blocked: no 2: phy0: Wireless LAN     Soft blocked: no     Hard blocked: no 3: hp-wwan: Wireless WAN     Soft blocked: no     Hard blocked: no   I have also searched about the status of the WiFi network being shown as disabled. Somehow everything pointed to the fact that my wireless device is switched off and it can be switched on from Windows only. However, I don't have windows partition and it has just Ubuntu 11.10 so I don't see any point in switching the device on in Windows. (Why) Has Kohonen-style SOM fallen out of favor? How to combine various armatures? “He is small enough to walk.” But baby wasn't walking so why didn't they use “small” instead of “small enough”? What statistical test to use for discrete predictor and response variables? I'm doing a statistical analysis of a model for college. It's modelling a bear catching fish and I'm asking will the amount of time taken to digest the fish have an effect on the amount of fish caught? (stupid question I know!) So the predictor variable is the amount of fish the bear can eat before it needs to digest and the response variable is the amount of fish it catches. The predictors varies between 1 and 30 in integers and the response is also in integers. I repeated each level of the predictor 5 times creating a sample size of 150 altogether. I was thinking of just using a simple correlation test such as cor.test in R, but I've read online that this is for continuous data. Does that matter or would this test still be appropriate? Thanks a million, Eamon How are the file metadata stored in Windows? (I'm using Windows XP but I guess it's similar in all the recent versions of Windows.)  When you create for example a new empty text document, you'll find in its properties that it has size of 0 bytes. Zero bytes means no information. No data. But still, the file has some name, it can still carry the dates of last access, modification and creation. It carries the information whether it's hidden file or not, whether it's read-only or not...  So where are all the metadata stored? How to remove enamel from wire? The app keeps asking for a nickname, and I have entered dozens of names, but it keeps saying that the names aren't available. How can I find an available name? How to distinguish between gold, silver, and bronze tag badges on SEDE? Consider the following sentence:     The labour-intensive and time-intensive part starts tomorrow.   I want to write this without rewriting the word "intensive."  Is this the correct way to do it?     The labour- and time-intensive part starts tomorrow.   Note the hyphen hanging after the word labour. Or should there be no hyphen after labour? Can anyone point me to a reference that talks about this? How to suppress Terminated message after killing in bash? The real fastest gun in the west Are the questions in the about page taken from real posts? If not, who designs them?  Particularly, why does this specific answer have a date from before the question was asked? When should I use "didn't" instead of "haven't"? Is haven't supposed to mean something I may still do and didn't not?  Can I use didn't for something I might still do? My wife wants a 4th baby, but I don't $P(\limsup A_n)=1 $ if $\forall A \in \mathfrak{F}$ s.t. $\sum_{n=1}^{\infty} P(A \cap A_n) = \infty$ Let $\mathfrak{F} = (A_n)_{n \in \mathbb{N}}$. Prove that $P(\limsup A_n)=1$ if $\forall A \in \mathfrak{F}$ s.t. $P(A) &gt; 0, \sum_{n=1}^{\infty} P(A \cap A_n) = \infty$. (Side question 1 Is second Borel-Cantelli out because we don't know if the $A_n$'s are independent?)  Suppose $\forall A \in \mathfrak{F}$ s.t. $P(A) &gt; 0, \sum_{n=1}^{\infty} P(A \cap A_n) = \infty$, but $P(\limsup A_n)&lt;1$. My prof gave us this convenient hint: Show $\exists M &gt; 0$ s.t. $P(\bigcap_{j=M}^{\infty} A_j^{c}) &gt; 0$.  $1 &gt; P(\limsup A_n)$  $1 - P(\limsup A_n) &gt; 0$  $P(\liminf A_n^{c}) &gt; 0$  By definition of $\liminf A_n^{c}$, $\exists M &gt; 0 $ s.t. $P(\bigcap_{j=M}^{\infty} A_j^{c}) &gt; 0$. (Side questions 2 and 3 Isn't this =1? ...Wait, is that what we're trying to prove? Haha)  $\to 1 - P(\bigcup_{j=M}^{\infty} A_j) &gt; 0$  $\to 1 &gt; P(\bigcup_{j=M}^{\infty} A_j)$  Main question: Now I guess we have to come up with some A s.t.  $\to 1 &gt; P(\bigcup_{j=M}^{\infty} A_j) \geq \sum_{n=1}^{\infty} P(A \cap A_n)$, or is there something else to do? Basically, here's my MWE, and I need to include "Chapter" before every section title in the ToC (without changing anything else).      \documentclass[12pt]{article} \usepackage[utf8]{inputenc}  \usepackage[english]{babel} \usepackage[titles]{tocloft} \usepackage{titlesec} \usepackage{titletoc}  \addto\captionsenglish{ \renewcommand*\contentsname{\centerline{TABLE OF CONTENTS}}}  %\renewcommand{\thesection}{CHAPTER} %\renewcommand{\cftsecpresnum}{Chapter \thesection} \titleformat{\section}[display]% {\null\vskip1em\sffamily\bfseries\filcenter}{Chapter \thesection}{0em}{}[] \titlespacing*{\section}{0em}{1em}{1em}  \titlecontents{section} [1.5em] % ie, 1.5em (chapter) + 2.3em {} {\contentslabel{1em}} {\hspace*{-1.5em}} {\titlerule*[0.5pc]{.}\contentspage}  \begin{document} \newpage \tableofcontents \newpage  \section{Section One} \section{Section Two} Content \end{document}   The commented out code is what I've already tried. The first one just changes the number to "CHAPTER" and doesn't move the text in the ToC (so it just overlays on top of the name of the section), and if I include "\thesection" after "CHAPTER" it creates an infinite loop definition error. The second one causes no differences, and the code still compiles.  Thanks! After the latest Win8.1x64 Updates, my system got stuck restarting or shutting down.. When I installed the last Windows update, all seemed fine except it got stuck doing the restart.  I waited about 5 minutes then used the power button.  Startup was normal.    But then when I told it to shut down it closed the programs then went to the "Shutting Down" screen and just stays there.    Disk activity lights aren't showing any activity.  Here is a screen grab of the most recent updates:    Before I do anything I wanted some input.  Question:  Any ideas of how I can figure out how to fix it? Trying to search for multiple file extensions in command line I am trying to find two extensions in command line but when i do it will only return one of the extensions. can you tell me what I am missing?   Here is my command;  [root]# find /etc -name "*.txt" -o -name "*.log" -type f -mtime +7 -exec echo {} \;