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Exercise 1.21 of Villani Topics in Optimal Transportation

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#measure-theory #optimization #calculus-of-variations #optimal-transport
1.1k
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Two random variables are independent if all continuous and bounded transformations are uncorrelated.

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#probability-theory #measure-theory #proof-verification #independence
118
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Proof Check: In a positive measure space, the measure of a union of an increasing chain of sets is equal to the limit of the measure of the sets.

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#real-analysis #measure-theory #proof-verification
731
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Completion of a measure space using null sets

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#real-analysis #measure-theory
176
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Proving lim inf means "all but a finite number" for measure theory

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#probability-theory #measure-theory #proof-writing
143
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Integral of an increasing function over subset of unit interval

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#measure-theory #lebesgue-integral #lebesgue-measure
141
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Why does the measure of a support $1$?

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#probability-theory #measure-theory #metric-spaces #borel-measures
1k
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Convergence both in $L^p$ and $L^q$

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#measure-theory #convergence-divergence #lp-spaces
212
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Why does such $M$ exist in this proof for Skorohod representation theorem?

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#probability-theory #measure-theory #metric-spaces
507
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Differential entropy vs Kolmogorov-Sinai "partition trick"

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#measure-theory #information-theory #entropy
33
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Borel-Cantelli-like inequality

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#measure-theory
651
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Proving the information inequality using measure theory

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#measure-theory #inequality #information-theory
1.3k
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Completion of measure spaces - uniqueness

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#real-analysis #measure-theory
456
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Is there only one complete measure extending Borel measure?

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#measure-theory #lebesgue-measure
523
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Is $\sigma((X,Y))=\sigma(X,Y)$?

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#probability-theory #measure-theory

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