Editing and manipulating tables with ArcPy?
Calculating well densities in selected counties using ArcPy?
Theorem. Let $(X,\mathcal B,\mu)$ a finite measure space, where $\mu$ is a positive measure. Let $\mathcal A\subset \mathcal B$ an algebra generating $\cal B$. Then for all $B\in\cal B$ and $\varepsilon&gt;0$, we can find $A\in\cal A$ such that $$\mu(A\Delta B)=\mu(A\cup B)-\mu(A\cap B)&lt;\varepsilon.$$  I don't think there is a proof in this site. It's a useful result for several reasons:  We know what the algebra generated by a collection of sets is, but not what the generated $\sigma$-algebra is. The map $\rho\colon \cal B\times\cal B\to \Bbb R_+$, $\rho(A,A')=\mu(A\Delta A')$ gives a pseudo-metric on $\cal B$. This makes a link between generating for an algebra and dense for the pseudo-metric. We say that a $\sigma$-algebra is separable if it's generated by a countable class of sets. In this case, the algebra generated by this class is countable. An with the mentioned result, we can show that $L^p(\mu)$ is separable for $1\leq p&lt;\infty$, which makes a link between the two notions. In ergodic theory, we have to test mixing conditions only an a generating algebra, not on all the $\sigma$-algebra. How to align prices in columns when both 2 digit and 4 digit variations of a price exist? Can I get from Gatwick airport to London by Oyster card? I read many contradictions as to whether one can use a Oyster card from Gatwick Airport to central London.  What is the most time-efficient way to go from Gatwick to "Old Billingsgate" (Monument tube station is nearby)? Public transportation is preferred over taxi. How to express a polar coordinate for a macro that only accepts space-separated values? \psElectricfield only accepts a coordinate in space-separated values as follows. For example, a charge of -0.1 unit at (-1,0) is written as [-0.1 -1 0]. I have attempted to write in PS notation but it still does not work.  \documentclass{article} \pagestyle{empty}  \usepackage{pst-electricfield,multido} \def\M{2}  \begin{document} \multido{\i=0+30}{12}{% \begin{pspicture*}(-\M,-\M)(\M,\M)     \psElectricfield     [         Q={[-0.1 -1 0][-0.1 1 0][0.1 !\i sin 2 mul \i cos 2 mul]}     ] \end{pspicture*}\newpage} \end{document}   How to express  a polar coordinate for a macro that only accepts space-separated values? A coin is tossed $n$ times. What is the probability of getting odd number of heads? A coin is tossed $n$ times. What is the probability of getting odd number of heads?   I started this chapter sometimes ago and faced in front of a tough problem. At first I started considering cases. Case-I : The probability of getting 1 head.Case-II : The probability of getting 3 head and so on. But there are many cases. So how can I solved this . Please help me. Thank you! After I saw that post i wanted to solve the first one which is $a\mid b^2,b^2\mid a^3,a^3\mid b^4,b^4\mid a^5\cdots$ Prove that $a=b$  Now i started by proving that $a$ and $b$ have same prime divisors,proving that is trivial,after doing so I checked do those factors have to have the same power.I tried with $$a=p^2,b=p^3$$ I noticed it exactly goes for 3 terms,or that $a^3\mid b^4$ doing $$a=p^{n-1},b=p^n\\p^{n-1}\mid p^{2n}\\p^{2n}\mid p^{3n-3}\\p^{3n-3}\mid p^{4n}\\p^{4n}\mid p^{5n-5}\\\cdots\\p^{n(n-1)}\mid p^{n(n-1)}\\p^{n(n-1)}\mid p^{n(n+1)}\\p^{n(n+1)}\not\mid p^{(n-1)(n+1)}$$ Now yeah I guess that would be a proof,but wouldn't setting $n=n+1$ infinitely many times make every term dividable? How can I repair the Windows 8 EFI Bootloader? Argument list too long for ls I get the following error when trying to ls *.txt | wc -l a directory that contains many files:  -bash: /bin/ls: Argument list too long   Does the threshold of this "Argument list" dependent on distro or computer's spec?  Usually, I'd pipe the result of such big result to some other commands (wc -l for example), so I'm not concerned with limits of the terminal. Should +1 and thanks comments be a declined flag? As a moderator for GD.SE I was always led to believe our role is to clean old comments as they are intended to be a temporary item depending on the level of context and if they add any benefit to an answer.  On SO I haven't had any issues or declines when I read old Q&amp;As and see +1 and thanks and flag.    However, on other sites when I read an old Q&amp;A and I see thanks or +1 I try to be courteous and flag them as I am aware moderators do get measured by their cleanup and I'm accustomed in doing so on SO but these flags are declined.    So this leads me to ask:   Should +1 and thanks comments be flagged and is the intended role of a comment still to be considered as temporary? What is the proper classification for a thanks or +1 comment if it should be flagged?   I didn't see any Q&amp;As on this topic after browsing the tags:   and searching led me to:  but that was several years old. Preservation of ideals in localized rings Refer to localization of rings in Lang's Algebra p. 108. In particular, let $A$ be a commutative ring, $S$ a subset of $A$ that is a submonoid of the multiplicative monoid structure of $A$, containing the identity. Then  $S^{-1}A$ is the set of elements $\frac{a}{s}$ with $a \in A$ and $s \in S$.  We have $\frac{a_1}{s_1}=\frac{a_2}{s_2}$ if there exists $\bar{s} \in S$ such that $\bar{s}(s_2a_1 - s_1 a_2)=0$. Now consider the injection of $A$ into $S^{-1}A$ given by $x \mapsto \frac{x}{1}$. This is a ring homomorphism. Let $J$ be an ideal of $A$. Ring homomorphisms preserve ideals and so the injection of $J$ into $S^{-1}A$, call it $J^{*}$, will be an ideal. My problem is that i don't see why for any $\frac{a}{s} \in S^{-1}A$ and any $\frac{j}{1} \in J^{*}$ we will have that $\frac{aj}{s}$ will be in $J^{*}$, i.e. why there must exist an element $\kappa \in J$ such that $\frac{aj}{s}=\frac{\kappa}{1}$. I'd say Microsoft have a way of bending the rules and I know that McLaren have won the championship. While this sounds strange, I believe it is correct English (sorry, I'm not native).   But when it's a small company, would you still use it this way? Is a company always plural, or are small companies singular? I.e., would you say Bakery Johnson makes fine bread or Bakery Johnson make fine bread? Is it My book seller, Woody's, have moved or is it has moved? How to use SSH to run a local shell script on a remote machine? I have to run a local shell script (windows/Linux) on a remote machine. I have SSH configured on both machine A and B. My script is on machine A which will run some of my code on a remote machine, machine B. The local and remote computers can be either Windows or Unix based system. Is there a way to run do this using plink/ssh? Phone Call On TextView Click How do I call a .NET assembly from C/C++? Suppose I am writing an application in C++ and C#.  I want to write the low level parts in C++ and write the high level logic in C#.  How can I load a .NET assembly from my C++ program and start calling methods and accessing the properties of my C# classes? What is postselection in quantum computing? A quantum computer can efficiently solve problems lying in the complexity class . I have seen a claim the one can (potentially, because we don't know whether BQP is a proper subset or equal to PP) increase the efficiency of a quantum computer by applying postselection and that the class of efficiently solvable problems becomes now postBQP = .  What does postselection mean here? On main and in the old mobile site (iirc) the username of the OP is highlighted in the comments.  This is no longer the case after the new design/theme was rolled out yesterday.  Can we get this back? No matter where I look, I just can't find gnome number [insert number here]. Where can I find every gnome in the game? This story had a researcher landing on an uncharted planet to see if it was any good for mining some type of mineral/metal.  Whilst there he encounters this type of ball that chases him all over the planet. He ends up finding this ball’s collection of other things it has caught including animals all the way back to the dinosaurs.  On the ball it has the writing '+/-7.  In the end it chases him for so long that he weighs too little for the balls 'collection'.  Any ideas greatly appreciated. Can I answer my own questions, even if I knew the answer before asking? I might want to answer my own question because:  I arrived at a solution before there were any other correct answers or I like mine better, can I still answer my own question?  I have a folder with lists of code snippets for things I always forget or get wrong, such as regular expressions for processing XML, common WinForms control idioms, etc. Is it considered poor etiquette for Stack Overflow to ask a question I already know the answer to, and then self answer, just so it gets recorded on the website?   Related:          For more information, see &quot;&quot; in the . A student is applying to a PhD program in Computer Sciences at Harvard and MIT. He estimates that he has two out of three chances of being accepted at Harvard and two out of five chances at MIT. He further estimates the probability that he will be accepted by both has probability of one to five. What is the probability that he is accepted by MIT if he is accepted by Harvard? Is the event "accepted by MIT" independent of the event "accepted by Harvard".  I don't understand if these are odds or probabilities