List questions from measurable-functions

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Show that $f$ is a Borel measurable function

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Checking the measurability of a function

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A function that is measurable on $(\mathbb{R}^n, \mathcal{B}(\mathbb{R}^n))$

Published on 30 Mar 2026 - 12:45

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How to show that a set is a sigma algebra

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$\int_K |u_n-u|^{p-\epsilon} \to 0$ implies that $\int_K|u_n-u|^p \to 0$

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If $f=g$ almost everywhere, then $\int_E f = \int_E g$.

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Lusin’s Theorem for Polish spaces with infinite Radon measure

Published on 23 Feb 2026 - 8:39

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Measurable function such that $f(af(x))$ is not measurable for any $a\ne0$

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Proof that $\int_X K(\cdot,y)f(y) \, d\mu(y)$ is measurable if $K, f\in L^2$?

Published on 15 Mar 2026 - 23:51

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Example of Non-Measurable Bijection from $\mathbb R \to \mathbb R$

Published on 09 Feb 2021 - 5:41

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How to show that $D$ is a Borel measurable set and $D_{f}$ is a Borel function.

Published on 29 Mar 2026 - 15:59

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Are Banach limits of measurable functions measurable?

Published on 14 Feb 2021 - 13:11

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$\mu$-measurable function $f$ and function $\bar{f}$

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Sufficient condition for measurability

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List Question

Independence of a finite number of random variables.

Show that $f$ is a Borel measurable function

Checking the measurability of a function

A function that is measurable on $(\mathbb{R}^n, \mathcal{B}(\mathbb{R}^n))$

How to show that a set is a sigma algebra

$\int_K |u_n-u|^{p-\epsilon} \to 0$ implies that $\int_K|u_n-u|^p \to 0$

If $f=g$ almost everywhere, then $\int_E f = \int_E g$.

Lusin’s Theorem for Polish spaces with infinite Radon measure

Measurable function such that $f(af(x))$ is not measurable for any $a\ne0$

Proof that $\int_X K(\cdot,y)f(y) \, d\mu(y)$ is measurable if $K, f\in L^2$?

Example of Non-Measurable Bijection from $\mathbb R \to \mathbb R$

How to show that $D$ is a Borel measurable set and $D_{f}$ is a Borel function.

Are Banach limits of measurable functions measurable?

$\mu$-measurable function $f$ and function $\bar{f}$

Sufficient condition for measurability

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