Is it possible to partition $[0, 1] = A \sqcup B$ such that given any $0 \leq x &lt; y \leq 1$, both $\mu([x,y] \cap A) &gt; 0$ and $\mu([x,y] \cap B) &gt; 0$?
This is from problem $8$, Chapter II of Rudin's Real and Complex Analysis.  The problem asks for a Borel set $M$ on $R$, such that for any interval $I$, $M \cap I$ has measure greater than $0$ and less than $m(I)$.  I was thinking of taking the Cantor approach: taking $R$ to be the union of $[a,b]$ with $a$ and $b$ rationals, and for each $[a,b]$ we construct Cantor sets inside it. During theconstruction of each Cantor set, in order to have positive measure on it, we need to take off smaller and smaller intervals from it, namely the proportion goes to $0$. As a result, these Cantor sets are extremely "dense" on their ends. If for an interval $I$ it intersects with the Cantor set on $[a,b]$ while $b-a&gt;&gt;m(I)$, we shall expect the measure of intersection to be rather close to $m(I)$ and then we lose control on these cases.  Is there any way to fix this or shall I consider other approaches?  Thank you
"#include" a text file in a C program as a char[] Is there a way to include an entire text file as a string in a C program at compile-time?  something like:   file.txt:  This is a little text file  main.c:  #include &lt;stdio.h&gt; int main(void) {    #blackmagicinclude("file.txt", content)    /*    equiv: char[] content = "This is\na little\ntext file";    */    printf("%s", content); }    obtaining a little program that prints on stdout "This is a little text file"  At the moment I used an hackish python script, but it's butt-ugly and limited to only one variable name, can you tell me another way to do it? If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$. can you help me to do a difference of CDF? I have 2 CDF's with equal number of points that I want to compare. These are from:   Temperature of 1 month from 2012 Mean temperature across months   What can I do to obtain this difference, this is from the formula of Finkelstein-Schafer PHP replaces spaces with underscores How can we connect a PHP script to MS Access (.mdb) file?  I tried by including following PHP code:  $db_path = $_SERVER['DOCUMENT_ROOT'] . '\WebUpdate\\' . $file_name . '.mdb'; $cfg_dsn = "Provider=Microsoft.Jet.OLEDB.4.0;Data Source=" . $db_path; $odbcconnect = odbc_connect($cfg_dsn, '', '');   But it failed and I received following error message:   Warning: odbc_connect() [function.odbc-connect]: SQL error: [Microsoft][ODBC Driver Manager] Data source name not found and no default driver specified, SQL state IM002 in SQLConnect in C:\web\WebUpdate\index.php on line 41 How can I prove that $\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain?  Also, I need to prove that its field of fractions is isomorphic to the field of rational functions $\mathbb{Q}(t)$?    (The question is taken from ) Attractive Boxed Equations I've got a very large document (which I've broken into "chapters" and such) which I've recently moved a few things around in.  Is there a nice way to get latex to output a list of forward references? (like, things in chapter 5 that reference a result in chapter 10) \foreach not behaving in axis environment Am hesitant to ask yet one more embarrassing question, but I can't seem to see the problem with the \foreach in the MWE. It should produce several horizontal lines but only produces the one with the yValue as specified in the \newcommand{\yValue}{0.3}:  Code: \documentclass{article} \usepackage{pgfplots}  \newcommand{\yValue}{0.3}  \begin{document} \begin{tikzpicture} \begin{axis} [  ymin=0,  ymax=1,  xmin=0,  xmax=1, ]  \foreach \yValue in {0.00,0.1,...,1.00} {     \draw [red] (axis cs:0,\yValue) -- (axis cs:1,\yValue); }  \end{axis} \end{tikzpicture} \end{document} cp - cannot create regular file : permission denied I want copy to /lib/udev but gives error  cp -f /tmp/ok_pcscd_hotplug.sh /lib/udev  cp:cannot create regular file /lib/udev/ok_pcscd_hotplug : Permission denied   I am root , but I can't understand . what can I do ? Macroscopic quantum phenomena and tunneling The company I work for has asked me to attend a training class on the other side of the country.  However my situation is my drivers license expired a few days ago. I do however have a separate printed email stating that the license has been renewed.  This drivers license is my only ID that shows both my name &amp; photo.  Is it possible to be able to board a flight with the expired drivers license and the printed email showing that it was renewed? I have only seen infinite vector spaces and the one finite vector space i.e the trivial vector space $\{0\}$. Is there any other finite vector space? The question is how can I exclude an object from the freestyle render?  What I need to do is create a Clay render with the wire only on the airplane.  My scene is simple I only have two objects the "Toy Plane" and the "floor". For the Clay render I only override the materials to a simple clay material and done.    But this happens when I use freestyle. How can I tell freestyle to ignore the "Floor"? Getting text from the Resource file in asp.net 4 What's wrong with this experiment showing that either FTL communication is possible or complementarity doesn't hold? The assumptions are:    Alice and Bob have perfectly synchronized clocks Alice and Bob have successfully exchanged a pair of entangled photons   The idea is simply to have Alice and Bob perform the Quantum Eraser Experiment (doesn't need to be the delayed choice).   Alice and Bob agree on a specific time when Bob's photon will be between the "path marker" (which is usually just after the slits) and the detector.  If Alice acts collpasing the wave-function on her photon, the interference pattern will disappear. If not it won't.  Alice and Bob can be spatially separated...  What am I misunderstanding?   The only meaningful difference from this spatially separated quantum eraser experiment to one done on tabletop is that you won't be able to use a coincidence detector, but that is not impeditive to identifying the interference pattern, just will make errors more probable. Which we should be able to deal with a appropriate protocol...  There is a experimental paper with a small amount of citations pointing out to the breaking of complementarity in a very similar setup: Rendering of Favorite/Ignored Tags in Firefox What is the "Wanna Cry" ransomware's possible impact on Linux users? It's just come to light that there's a $300 ransom you have to pay because ransomware targeting Microsoft Windows has encrypted your data. What steps do Linux users need to protect from this if for example they are using wine?  This ransomware is widely reported to be based on a tool developed by the NSA to hack into computers. The NSA tool was used by a hacker group called the Shadow Brokers. The code can be found in .  Microsoft released a patch (MS17-010) against this vulnerability on March 14, 2017. The mass infection is reported to have begun spreading on April 14th. This is discussed .  As I haven't booted Windows 8.1 in 6 to 8 weeks, can I apply this patch from Ubuntu without booting Windows first? (After research it may be possible ClamAV could report the vulnerability from the Linux side looking into Windows partition but it's unlikely it could apply the patch. The best method would be to reboot into Windows and apply patch MS17-010.)  Individuals and small companies who subscribe to Microsoft Automatic Updates are uninfected. Larger organizations who delay apply patches as they are tested against organization intranets are more likely to be infected.  On May 13, 2017, Microsoft took the extraordinary step of releasing a patch for Windows XP which has been unsupported for 3 years.  No word if wine is doing anything about a security update. It was reported in a comment below that Linux can be infected too when users run .  An  registered a domain name that acted as a kill-switch to the ransomware. I presume the non-existent domain was used by the hackers on their private intranet so they didn't infect themselves.  Next time they will be smarter so don't rely on this current kill-switch. Installing the Microsoft patch, which prevents exploiting a vulnerability in the SMBv1 protocol, is the best method.  On May 14, 2017 Red Hat Linux said they are not affected by "Wanna Cry" ransomware. This might mislead Ubuntu users along with Red Hat, CentOS, ArchLinux and Fedora users. Red Hat supports wine which answers below confirm can be effected. In essence Ubuntu and other Linux distro users googling this issue might be mislead by the Red Hat Linux Support answer .  May 15, 2017 Update. Over the last 48 hours Microsoft released patches called KB4012598 for  to protect against "Wanna Cry" ransomware. These Windows versions are no longer on automatic updates. Although I applied security update MS17-010 on my Windows 8.1 platform yesterday, my old Vista Laptop still needs patch KB4012598 downloaded and manually applied.       Moderator note: This question is not off topic - it asks about whether or not any Linux users need to do any steps for protecting against the risk.      It is perfectly on topic here, because it's relevant to Linux (which Ubuntu is), and it's also relevant for Ubuntu users running Wine or similar compatibility layers, or even VMs on their Ubuntu Linux machines. Effective way to find any file's Encoding Upgrade to the latest PHP version in ubuntu 16.04