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Prove that the measure-theoretic definition of probability aligns with the basic one?

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#probability #measure-theory #conditional-expectation
27
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Domain of integral with respect to probability law.

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#probability #integration #probability-theory #measure-theory
1.1k
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Proof that conditional expectation is defined uniquely almost everywhere?

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#measure-theory
114
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Question about vitali set

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#measure-theory
133
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$\sigma$ algebra and sets of measure $0$

Published on
#measure-theory #lebesgue-measure
137
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Converse of Comparison Theorems for Lebesgue Integrals

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#real-analysis #measure-theory #lebesgue-integral
2.2k
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Why is an uncountable union of null sets not necessarily a null set?

Published on
#real-analysis #measure-theory #soft-question #terminology
856
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Understanding what the sigma-field should be in dice-experiment

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#measure-theory
97
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About definition of Ergodic theorem

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#measure-theory #operator-theory #ergodic-theory
2.3k
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What is a jump function, and which measure does it induce?

Published on
#probability-theory #measure-theory #lebesgue-integral #stieltjes-integral
93
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Doubt about the RADEMACHER'S THEOREM demonstration.

Published on
#real-analysis #measure-theory #lebesgue-measure #partial-derivative
145
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Continuity of probability measure from below - proof

Published on
#measure-theory
666
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Question about particular proof of the translation invariance of the Lebesgue outer measure.

Published on
#measure-theory
351
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Hausdorff measure of a smooth curve

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#integration #measure-theory #hausdorff-measure
505
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Example of measures being ergodic but not invariant

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#measure-theory #operator-theory #ergodic-theory

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