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extremal010101.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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alanrendall.wordpress.com
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| | | | | The theorem of the title is about dividing smooth functions by other smooth functions or, in other words, representing a given smooth function in terms of products of other smooth functions. A large part of the account which follows is based on that in the book 'Normal Forms and Unfoldings for Local Dynamical Systems' by... | |
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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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mmph.wordpress.com
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| | | The recent post on cloud computing and Google Docs made me ask myself whether Google Docs supports (La)TeX. It turned out you can insert LaTeX equations into your Google doc (as discussed in more detail e.g. here) but that's that for now. There exists a LaTeX Lab project aspiring to develop a web-based LaTeX editor... | ||
