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datuan5pdes.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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bomongiaitich.wordpress.com
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| | | | | Nh?c l?i b?t ?ng th?c Holder: Cho $latex 1\le p, p' \le \infty$ th?a mãn $latex 1/p + 1/p'=1.$ L?u ý tr?ng h?p $latex p=1, p'=\infty$ và $latex p=\infty, p'=1.$ Xét không gian ?o $latex (\Omega, \mathcal B, \mu)$, và $latex f\in L^p(\Omega, \mu), g\in L^{p'}(\Omega, \mu).$ Khi ?ó $latex fg\in L^1(\Omega, \mu)$ và... | |
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eklausmeier.goip.de
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qchu.wordpress.com
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| | | As a warm-up to the subject of this blog post, consider the problem of how to classify$latex n \times m$ matrices $latex M \in \mathbb{R}^{n \times m}$ up to change of basis in both the source ($latex \mathbb{R}^m$) and the target ($latex \mathbb{R}^n$). In other words, the problem is todescribe the equivalence classes of the... | ||
