List questions from measure-theory

Published on 14 Apr 2026 - 11:58

162

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Let $\Omega = R$ and show that $\mathscr{F}=\big\{A: A$ is countable or $A^c$ is countable$\big\}$ is a $\sigma$-field.

Published on 15 Apr 2026 - 18:21

108

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Prove that $\mu^(A) + \mu^(A^c)=1$ if and only if for every $\epsilon>0$, there exists $E\in \mathcal A$ such that $\mu^*(A\Delta E) < \epsilon$

Published on 16 Apr 2026 - 9:07

451

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Proof verification $C[a,b]$ is dense in $L^p[a,b]$

Published on 13 Apr 2026 - 5:06

85

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Why does the sigma algebra generated by a rectangle include one side of a number line?

Published on 15 Apr 2026 - 11:12

39

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Do subset sigma algebras exist in general?

Published on 11 Apr 2026 - 21:20

223

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How to remember $\limsup$ and $\liminf$ of sets

Published on 14 Apr 2026 - 7:32

43

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Proving the measure of a set is between 0 and $2\epsilon$ using Countable Sub-additivity

Published on 15 Apr 2026 - 15:24

783

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Showing that a set is dense in the real numbers.

Published on 12 Apr 2026 - 14:41

108

Views

Is it possible for a sequence of sets $A_{1}$, $A_{2}$, $A_{3}, ... \in \mathscr{F} $ to all be disjoint, AND all be countably infinite sets?

Published on 16 Apr 2026 - 14:38

110

Views

Measurable function on Hilbert space

Published on 11 Apr 2026 - 15:52

76

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Rational translates of Fat Cantor set as positive but not full measure for each interval

Published on 13 Apr 2026 - 14:59

274

Views

Is a density nonnegative almost everywhere?

Published on 08 Apr 2026 - 20:37

292

Views

Compute norm of linear functional

Published on 08 Apr 2026 - 14:39

39

Views

relation between the moments of distributions

Published on 10 Apr 2026 - 18:15

List Question

Family of Measurable Sets Implies Measurable Function

Let $\Omega = R$ and show that $\mathscr{F}=\big\{A: A$ is countable or $A^c$ is countable$\big\}$ is a $\sigma$-field.

Prove that $\mu^(A) + \mu^(A^c)=1$ if and only if for every $\epsilon>0$, there exists $E\in \mathcal A$ such that $\mu^*(A\Delta E) < \epsilon$

Proof verification $C[a,b]$ is dense in $L^p[a,b]$

Why does the sigma algebra generated by a rectangle include one side of a number line?

Do subset sigma algebras exist in general?

How to remember $\limsup$ and $\liminf$ of sets

Proving the measure of a set is between 0 and $2\epsilon$ using Countable Sub-additivity

Showing that a set is dense in the real numbers.

Is it possible for a sequence of sets $A_{1}$, $A_{2}$, $A_{3}, ... \in \mathscr{F} $ to all be disjoint, AND all be countably infinite sets?

Measurable function on Hilbert space

Rational translates of Fat Cantor set as positive but not full measure for each interval

Is a density nonnegative almost everywhere?

Compute norm of linear functional

relation between the moments of distributions

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