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www.encyclopediaofmath.org
| | ncatlab.org
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| | alanrendall.wordpress.com
3.5 parsecs away

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| | In a previous post I discussed the Brouwer fixed point theorem and I mentioned the fact that it applies to any non-empty closed bounded convex subset of a Euclidean space, since a subset of this kind is homeomorphic to a closed ball in a Euclidean space. However I did not prove the latter statement. I...
| | 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...
| | cosmiaineurope.wordpress.com
12.3 parsecs away

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| Cosmia's travel in Europe from June 2018 to July 2018