List questions from measure-theory

Published on 10 May 2026 - 14:40

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Measure and metric

Published on 13 Apr 2026 - 3:45

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The action of $SO(n + 1)$ on $S^n$ is ergodic

Published on 11 May 2026 - 8:56

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$\mathrm {Var}(X)=\mathrm E(X|\mathcal B)+\mathrm E[X-\mathrm E(X|\mathcal B)]^2\Rightarrow \mathrm {Var}(E(X|\mathcal B)))\le\mathrm {Var}(X)$

Published on 16 Apr 2026 - 6:40

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Lebesgue Measurable via open set

Published on 13 Apr 2026 - 21:46

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Not $\sigma$-compact set without axiom of choice

Published on 14 May 2026 - 14:26

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The Convergence of Convolution of $f$ and $g$

Published on 10 May 2026 - 16:34

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$\int_{[-1,1]}\int_{[-1,1]}\frac{xy}{(x^2+y^2)^2}d\lambda(x) d\lambda(y)= \int_{[-1,1]}\int_{[-1,1]}\frac{xy}{(x^2+y^2)^2}d\lambda(y) d\lambda(x)$

Published on 17 Apr 2026 - 13:21

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Expected value of non-negative bounded random variable

Published on 10 Apr 2026 - 5:07

162

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Is the graph of integrable function a Jordan set

Published on 14 Apr 2026 - 11:06

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cover of $\mathbb{R^n}$

Published on 13 Apr 2026 - 12:33

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Is a monotone class which is closed under complements and finite disjoint unions a sigma-algebra?

Published on 10 Apr 2026 - 23:09

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Can ergodicity be checked by restricting attention to continuous maps?

Published on 11 May 2026 - 8:54

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What are $\delta$-shock solutions?

Published on 10 May 2026 - 19:27

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$X\in L^2$ implies $Y:=(X-E[X])^2 \in L^1$

Published on 16 Apr 2026 - 1:46

List Question

$\int_Xfgd\mu=0\;\forall g$ in a dense subset of $L^q\Rightarrow f=0$ a.e.

Measure and metric

The action of $SO(n + 1)$ on $S^n$ is ergodic

$\mathrm {Var}(X)=\mathrm E(X|\mathcal B)+\mathrm E[X-\mathrm E(X|\mathcal B)]^2\Rightarrow \mathrm {Var}(E(X|\mathcal B)))\le\mathrm {Var}(X)$

Lebesgue Measurable via open set

Not $\sigma$-compact set without axiom of choice

The Convergence of Convolution of $f$ and $g$

$\int_{[-1,1]}\int_{[-1,1]}\frac{xy}{(x^2+y^2)^2}d\lambda(x) d\lambda(y)= \int_{[-1,1]}\int_{[-1,1]}\frac{xy}{(x^2+y^2)^2}d\lambda(y) d\lambda(x)$

Expected value of non-negative bounded random variable

Is the graph of integrable function a Jordan set

cover of $\mathbb{R^n}$

Is a monotone class which is closed under complements and finite disjoint unions a sigma-algebra?

Can ergodicity be checked by restricting attention to continuous maps?

What are $\delta$-shock solutions?

$X\in L^2$ implies $Y:=(X-E[X])^2 \in L^1$

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