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I'm trying to learn more mathematics and am especially interested in analysis and probability.

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On the existence of a family of countably additive extensions of Lebesgue measure

set-theory measure-theory lebesgue-measure asked Dec 19, 2019 at 5:36

mathoverflow.net

12 votes

What is the weak*-topology on a set of probability measures?

general-topology functional-analysis probability-theory measure-theory reference-request asked Jan 24, 2017 at 3:25

math.stackexchange.com

12 votes

Convergence in distribution of conditional expectations

probability-theory reference-request martingales central-limit-theorem probability-limit-theorem asked May 19, 2017 at 1:24

math.stackexchange.com

11 votes

How to explain connections between bounded Radon-Nikodym derivatives, convex combinations of probabilities, and conditional probability

probability-theory measure-theory asked Mar 21, 2017 at 0:24

math.stackexchange.com

11 votes

A set in the Borel $\sigma$-algebra over $[0,1]$ that isn't in the algebra generated by open sets

general-topology measure-theory borel-sets asked Nov 4, 2020 at 8:29

math.stackexchange.com

10 votes

How to prove the Lebesgue density theorem using martingales?

real-analysis probability-theory measure-theory martingales asked Jul 13, 2017 at 0:08

math.stackexchange.com

9 votes

Probability of choosing integers that sum to zero

probability number-theory asked Jan 25, 2020 at 22:58

math.stackexchange.com

9 votes

Setwise convergence with martingales

real-analysis probability-theory measure-theory martingales asked May 24, 2017 at 0:34

math.stackexchange.com

9 votes

If a strictly convex function attains a minimum on the unit ball, does it attain a minimum on every weak*-compact set?

functional-analysis convex-analysis convex-optimization topological-vector-spaces asked Dec 20, 2020 at 9:26

math.stackexchange.com

9 votes

Does a generalization of Tietze's extension theorem hold for set-valued functions?

reference-request gn.general-topology continuity set-valued-analysis asked Aug 3, 2020 at 5:59

mathoverflow.net

Top Answers

$S$ is closed under pairwise unions $⇒$ $S$ is closed under arbitrary unions?

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What do Commas Mean in Probability

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What's objectionable about the Axiom of Countable Additivity?

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Negation of $0 = 1$

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Are there continuous functions for which the epsilon-delta property doesn't hold?

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How do I think of a measurable function?

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Show a set E is measurable iff its characteristic function is measurable.

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Probability of picking an odd number from the set of naturals?

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For the statement A implies B, write the statement NOT B implies NOT A.

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The conditional expectation of an almost surely positive random variable

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The additivity axiom of probabiity

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How to determine if two lines are parallel/ almost parallel?

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In Royden, a set $E$ is measurable iff $m(E \triangle U) < \epsilon$ where $U$ is a finite union of intervals

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Looking for a very gentle first book on Measure Theoretic probability

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Prove that $P(X\leq Y)=1$ implies $F_Y \leq F_X$

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Lebesgue Dominated Convergence Theorem

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Multiple Applications of Bayes' Theorem

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Prove that $\sin X_n$ converges in probability

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Inner regular content is premeasure

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Prove $[0,1]$ is closed using the definition of all sequences converge to their limit points.

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Question on the use of the Markov Kernel for conditional probability

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