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\|	\|	jmanton.wordpress.com Some Comments on the Situation of a Random Variable being Measurable with respect to the Sigma-Algebra Generated by Another Random Variable \| Jonathan Manton's Blog	1.6 parsecs away Travel
\|	\|	If $latex Y$ is a $latex \sigma(X)$-measurable random variable then there exists a Borel-measurable function $latex f \colon \mathbb{R} \rightarrow \mathbb{R}$ such that $latex Y = f(X)$. The standard proof of this fact leaves several questions unanswered. This note explains what goes wrong when attempting a "direct" proof. It also explains how the standard proof...	1.6 parsecs away Travel
\|	\|	lucatrevisan.wordpress.com Online Optimization Post 6: The Impagliazzo Hard-Core Set Lemma \| in theory	6.3 parsecs away Travel
\|	\|	(This is the sixth in a series of posts on online optimization techniques and their ``applications'' to complexity theory, combinatorics and pseudorandomness. The plan for this series of posts is to alternate one post explaining a result from the theory of online convex optimization and one post explaining an ``application.'' The first two posts were...	6.3 parsecs away Travel
\|	\|	jaywillmath.wordpress.com Universal countable Borel equivalence relations with an eye toward finitely generated groups \| jaywillmath	6.2 parsecs away Travel
\|	\|	In the previous post, I discussed a technique due to Neumann and Neumann for embedding any countable group into a 2-generated group, and mentioned in passing that they used the same ideas to create a finitely generated 3-solvable non-Hopfian group. This construction turned out to be very useful to my own research, but to describe...	6.2 parsecs away Travel
\|	\|	vitalyobukhov.wordpress.com Shurali the cat \| #about.me	24.1 parsecs away Travel
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