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almostsuremath.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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extremal010101.wordpress.com
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| | | | | Suppose we want to understand under what conditions on $latex B$ we have $latex \begin{aligned} \mathbb{E} B(f(X), g(Y))\leq B(\mathbb{E}f(X), \mathbb{E} g(Y)) \end{aligned}$holds for all test functions, say real valued $latex f,g$, where $latex X, Y$ are some random variables (not necessarily all possible random variables!). If $latex X=Y$, i.e., $latex X$ and $latex Y$ are... | |
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terrytao.wordpress.com
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| | | | | In preparation for my upcoming course on random matrices, I am briefly reviewing some relevant foundational aspects of probability theory, as well as setting up basic probabilistic notation that we... | |
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matthewmcateer.me
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| | | Important mathematical prerequisites for getting into Machine Learning, Deep Learning, or any of the other space | ||
