How can I do string replace with lambda function in Java
Java equivalent to PHP's preg_replace_callback
Python: Uniqueness for list of lists Intuition behind the definition of a measurable set This week I saw the definition of a measurable set for an outer measure.     Let $\mu^*$ be an outer measure on a set $X$. We call $A \subseteq X$ measurable if $$\mu^*(E) = \mu^*(A\cap E) + \mu^*(A^c\cap E)$$ for every $E \subseteq X$.   This is not the first time I've seen this definition. Unlike most other things in mathematics, over time I have gained absolutely no intuition as to why this is the definition.   The only explanation I've ever seen is that a set is measurable if it 'breaks up' other sets in the way you'd want. I don't really see why this is the motivation though. One reason I am not comfortable with it is that you require a measurable set to break up sets which, according to this definition, are non-measurable; why would you require that? Of course, you can't say what a non-measurable set is without first defining what it means to be measurable so I suppose no matter what your condition is, it will have to apply to all subsets of $X$.     Is there an intuitive way to think about the definition of measurable sets? Is there a good reason why we should use this definition, aside from "it works"? How do i make my ubuntu server public? I want to know how to make my ubuntu server ip public. I'm not asking for a domain, if people would be able to access my website by ip, it would be great! (just for now) Does someone have an idea how to do this? Can I ignore coefficients for non-significant levels of factors in a linear model? After seeking clarification about linear model coefficients  I have a follow up question concerning non-signficant (high p value) for coefficients of factor levels.  Example: If my linear model includes a factor with 10 levels, and only 3 of those levels have significant p values associated with them, when using the model to predict Y can I choose to not include the coefficient term if the subject falls in one of the non-signficant level?  More drastically, would it be wrong to lump the 7 non-significant levels into one level and re-analyze? JavaScript property access: dot notation vs. brackets? How to create a matrix with 20 columns in latex The code below works,  but when I add 10 more columns, it does not. So, how can I add ten more columns to the matrix below?  \documentclass{article} \usepackage{amsmath} \begin{document}  \begin{equation} \begin{bmatrix}  1 &amp; 0 &amp; 0 &amp; 0  &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 1 &amp; 0  \end{bmatrix} \end{equation}  \end{document} How can I save application settings in a Windows Forms application? Prove that the derivative of an even differentiable function is odd, and the derivative of an odd is even. Relativity and Galaxy Rotation Speed I was browsing flight price at Singapore Airlines website, and a one-way flight from SIN to SFO cost this much:    That's quite expensive. I tried browsing around and found that a return flight from SFO to SIN and back to SFO cost much cheaper:    It's really weird because the second ticket includes the exact same flight that cost 1900+, but it's almost half the price. The reason for this counter-intuitive situation is explained in the answers this question   If I am located in Singapore and my intention is to fly one-way to SFO, is it safe to book the flight in the second picture and only board SFO-SIN leg? Will they deny me because I miss the SIN-SFO flight? Find all Facebook comments on external websites Is there any way to find all comments on external websites connected with a Facebook account? Let's say I want to find all my Facebook activity on external pages based on profile URL; is there any way to do this? Another simple series convergence question: $\sum\limits_{n=3}^\infty \frac1{n (\ln n)\ln(\ln n)}$ I'm being asked to determine if $\displaystyle\sum\limits_{n=3}^\infty \frac1{n (\ln n)\ln(\ln n)}$ converges. So, using Cauchy's Condensation Test, I reduced the problem to one of determining the convergence of $\displaystyle\sum\limits_{n=3}^\infty\frac 1{n\ln (n\ln 2)}$. Am I on the right path, and how do I proceed from here? Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic. Let $f$ be  a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.  Suppose that $f$ is not monotonic.Then $\exists a,b;a&gt;b$ such that $f(a)&lt;f(b)$ and $c,d;c&lt;d$ such that $f(c)&gt;f(d)$.Since $f$ is continuous then there exists no break in the graph of $f$. But how should I use the fact that $f$ is open.Any help on how should I do the proof? I've noticed that, if I add \n to a pattern for substituting using sed, it does not match. Example:  $ cat &gt; alpha.txt This is a test Please do not be alarmed  $ sed -i'.original' 's/a test\nPlease do not/not a test\nBe/' alpha.txt  $ diff alpha.txt{,.original}  $ # No differences printed out   How can I get this to work? So I have a Palm Pre (original P100EWW) model that I enabled developer mode on, and installed a Debian Squeeze chroot.  Works great.  I have plans to use this for ANYTHING (bittorrent peer, web server) but a phone.  I noticed if I do a cat /dev/urandom &gt; /dev/fb0 it actually writes random pixels to the screen until a No space left on device error is generated.  Awesome, now I can use the display.  So what kind of utilites are there that will either A) let me use /dev/fb0 as a console I can output text to or B) render text on /dev/fb0 from the command line.  I don't know about recompiling the kernel for this yet (I'd love to eventually strip WebOS off entirely and turn this into a minimal ARM server) so userspace tools if they exist is what I'm asking about.  Also would prefer to render directly to /dev/fb0 and not use X. Can "what kind" be plural? Is it correct to say, "What kind of patents are being issued in these sophisticated times?" It seems like it should be What kind of patents is being issued..., but that sounds wrong.  What kind of patent is being issued... is correct and sounds right, but loses a little bit of the original meaning.  Is there something magic about what kind that allows it to be plural, or do people just misuse it a lot? Drawing a square root spiral Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials? Let $ A, B $ be two square matrices of order $n$. Do $ AB $ and $ BA $ have same minimal and characteristic polynomials?   I have a proof only if $ A$ or $ B $ is invertible. Is it true for all cases? I am running Ubuntu 18.04. I wanted to install node and npm on my machine. The apt repository version of node is 8.x, whereas I wanted to have version 12.x (Current LTS version).  I followed the guide here:   As per the guide, I downloaded curl -sL https://deb.nodesource.com/setup_12.x -o nodesource_setup.sh  and then ran it with sudo -E ./nodesource_setup.sh    However, my machine fails to run sudo apt update with the following (full) output:  maxim@fujitsu:~/scripts$ sudo apt update Hit:1 http://gb.archive.ubuntu.com/ubuntu bionic InRelease                  Hit:2 http://gb.archive.ubuntu.com/ubuntu bionic-updates InRelease          Get:3 http://security.ubuntu.com/ubuntu bionic-security InRelease [88.7 kB] Hit:4 http://gb.archive.ubuntu.com/ubuntu bionic-backports InRelease               E: Repository 'http://security.ubuntu.com/ubuntu bionic-security InRelease' changed its 'Suite' value from 'bionic-updates' to 'bionic-security' N: This must be accepted explicitly before updates for this repository can be applied. See apt-secure(8) manpage for details. Do you want to accept these changes and continue updating from this repository? [y/N] N Fetched 88.7 kB in 8s (10.5 kB/s)                                                       Reading package lists... Done E: Failed to fetch http://security.ubuntu.com/ubuntu/dists/bionic-security/InRelease   E: Some index files failed to download. They have been ignored, or old ones used instead.    suggests that one should use apt update instead of apt-get update. None the less, I am running apt update.   suggests to answer "Y" to the prompt.  , from the Docker community, makes it clear that doing so is a bad idea.  However, , suggests that sometimes repositories change the names of package sources.  So my question is, is it OK to answer Y here? I don't want to  just blindly accept whatever error the package manager throws at me. I need to process a large file, around 400K lines and 200 M. But sometimes I have to process from bottom up. How can I use iterator (yield return) here? Basically I don't like to load everything in memory. I know it is more efficient to use iterator in .NET.