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almostsuremath.com
| | djalil.chafai.net
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| | [AI summary] A mathematical deep dive into the Wintner-Kosulajeff-Tukey phenomenon explaining how the fractional part of scaled random variables converges to a uniform distribution.
| | terrytao.wordpress.com
4.0 parsecs away

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| | Thus far, we have only focused on measure and integration theory in the context of Euclidean spaces $latex {{\bf R}^d}&fg=000000$. Now, we will work in a more abstract and general setting, in w...
| | jmanton.wordpress.com
2.3 parsecs away

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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...
| | emiruz.com
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