List questions from measure-theory

Published on 09 Apr 2026 - 9:09

51

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Size of the maximal function $f^*$

Published on 14 Apr 2026 - 19:23

57

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Discrete time process vs Markov chain.

Published on 12 Apr 2026 - 18:31

1.3k

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How to define a measure as a difference of two measures

Published on 08 Apr 2026 - 17:53

30

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Proof of unicity of $Z$ s.t. $\int_G Zd\mathbb P=\int_G d\mathbb P$.

Published on 16 Apr 2026 - 9:53

181

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Euclidean Measure on Unit Sphere in $\Bbb{C}^n$

Published on 12 Apr 2026 - 3:13

587

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Lebesgue measure of the open unit cube

Published on 12 Apr 2026 - 3:33

36

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Is $\lambda_2(B\times\mathbb{R})$ on the sigma algebra $\sigma:=\{B \times \mathbb{R}:B\in\mathcal{B}\}$ sigma-finite?

Published on 15 Apr 2026 - 0:52

153

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Is the product of two random variables finite if the expectation of the random variables squared is finite?

Published on 13 Apr 2026 - 19:18

57

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Show $\sigma ( \tau) = \sigma ( A)$ as an alternative formulation of Borel $\sigma -$Algebra

Published on 16 Apr 2026 - 9:31

36

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Probability kernel defined as quotient of integrals of joint density functions

Published on 11 Apr 2026 - 14:20

52

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Show that $i(f) = \int_a^b f \,d\lambda$ and $s(f) = \int_a^b f \,d\lambda$

Published on 17 Apr 2026 - 9:59

83

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Is $E(Y|X)=0, a.s.$ equivalent to $E[Y\cdot f(X)]=0, \forall f\in \mathscr{B}$?

Published on 15 Apr 2026 - 9:25

46

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Function is measurable iff fn is measurable

Published on 13 Apr 2026 - 23:30

444

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Using Dominated Convergence Theorem to interchange Integral and Taylor Series of Sine

Published on 11 Apr 2026 - 16:57

List Question

Convergence in measure: two definitions

Size of the maximal function $f^*$

Discrete time process vs Markov chain.

How to define a measure as a difference of two measures

Proof of unicity of $Z$ s.t. $\int_G Zd\mathbb P=\int_G d\mathbb P$.

Euclidean Measure on Unit Sphere in $\Bbb{C}^n$

Lebesgue measure of the open unit cube

Is $\lambda_2(B\times\mathbb{R})$ on the sigma algebra $\sigma:=\{B \times \mathbb{R}:B\in\mathcal{B}\}$ sigma-finite?

Is the product of two random variables finite if the expectation of the random variables squared is finite?

Show $\sigma ( \tau) = \sigma ( A)$ as an alternative formulation of Borel $\sigma -$Algebra

Probability kernel defined as quotient of integrals of joint density functions

Show that $i(f) = \int_a^b f \,d\lambda$ and $s(f) = \int_a^b f \,d\lambda$

Is $E(Y|X)=0, a.s.$ equivalent to $E[Y\cdot f(X)]=0, \forall f\in \mathscr{B}$?

Function is measurable iff fn is measurable

Using Dominated Convergence Theorem to interchange Integral and Taylor Series of Sine

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