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A VERY BRIEF REVIEW OF MEASURE THEORY
A brief philosophical discussion:
Measure theory, as much as any branch of mathematics, is an area where it is important to be acquainted with the basic notions and statements, but not desperately important to be acquainted with the detailed proofs, which are often rather unilluminating. One should always have in a mind a place where one could go and look if one ever did need to understand a proof: for me, that place is Rudin’s Real and Complex Analysis (Rudin’s “red book”).
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february 2017 by nhaliday
Shtetl-Optimized » Blog Archive » Logicians on safari
So what are they then? Maybe it’s helpful to think of them as “quantitative epistemology”: discoveries about the capacities of finite beings like ourselves to learn mathematical truths. On this view, the theoretical computer scientist is basically a mathematical logician on a safari to the physical world: someone who tries to understand the universe by asking what sorts of mathematical questions can and can’t be answered within it. Not whether the universe is a computer, but what kind of computer it is! Naturally, this approach to understanding the world tends to appeal most to people for whom math (and especially discrete math) is reasonably clear, whereas physics is extremely mysterious.

the sequel: http://www.scottaaronson.com/blog/?p=153
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january 2017 by nhaliday
Talagrand’s concentration inequality | What's new
Proposition 1 follows easily from the following statement, that asserts that if a convex set {A \subset {\bf R}^n} occupies a non-trivial fraction of the cube {\{-1,+1\}^n}, then the neighbourhood {A_t := \{ x \in {\bf R}^n: \hbox{dist}(x,A) \leq t \}} will occupy almost all of the cube for {t \gg 1}:
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may 2016 by nhaliday

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