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mkatkov.wordpress.com | ||
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jmanton.wordpress.com
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| | | | | 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... | |
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thehighergeometer.wordpress.com
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| | | | | Here's a fun thing: if you want to generate a random finite $latex T_0$ space, instead select a random subset from $latex \mathbb{S}^n$, the $latex n$-fold power of the Sierpinski space $latex \mathbb{S}$, since every $latex T_0$ space embeds into some (arbitrary) product of copies of the Sierpinski space. (Recall that $latex \mathbb{S}$ has underlying... | |
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extremal010101.wordpress.com
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| | | | | With Alexandros Eskenazis we posted a paper on arxiv "Learning low-degree functions from a logarithmic number of random queries" exponentially improving randomized query complexity for low degree functions. Perhaps a very basic question one asks in learning theory is as follows: there is an unknown function $latex f : \{-1,1\}^{n} \to \mathbb{R}$, and we are... | |
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mikiobraun.wordpress.com
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| | | Under construction till I find some time to put some stuff here... ;) | ||
