List questions from lebesgue-measure

Published on 24 Apr 2026 - 9:38

176

Views

if $\mu(X)$ is finite and $f$ is finite on X a.e then $\lim_{n\to \infty}\mu \{x: |f(x)|\geq n\}=0$

Published on 24 Apr 2026 - 9:50

172

Views

Number of equivalence classes of functions of real variable with the a.e relation.

Published on 16 Apr 2026 - 13:49

160

Views

Is the completion of a measure space necessary?

Published on 12 Apr 2026 - 11:55

97

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Showing a certain function vanishes almost everywhere

Published on 24 Apr 2026 - 9:36

309

Views

$\mu(A \cap I) \le a \mu(I)$ implies $\mu(A) = 0$?

Published on 12 Apr 2026 - 13:50

368

Views

Showing continuous functions are dense in $L^p([0,1],\lambda)$, where $\lambda$ is Lebesgue measure

Published on 17 Apr 2026 - 22:32

989

Views

Borel measure induced by the Cantor function?

Published on 12 Apr 2026 - 20:06

26

Views

existence of a sequence of continuous functions with two conditions

Published on 17 Apr 2026 - 5:30

44

Views

Find the limit $\lim \int_{(0,1]} f_n \, d\lambda $ where $ \lambda $ is lebesgue measure

Published on 24 Apr 2026 - 11:22

672

Views

Lebsegue measure of $\{ 0<x \leq 1: x \sin \left(\frac{\pi}{2x}\right) \geq 0 \}$

Published on 16 Apr 2026 - 2:55

2.1k

Views

Properties of decreasing sequence of Lebesgue measurable sets.

Published on 10 Apr 2026 - 13:27

156

Views

L'Hôpital with absolute continuity

Published on 24 Apr 2026 - 11:21

436

Views

Repeated extension of Lebesgue measure

Published on 10 Apr 2026 - 7:38

443

Views

Property of a set of a positive Lebesgue measure

Published on 14 Apr 2026 - 3:48

List Question

Mean value theorem for Lebesgue integral

if $\mu(X)$ is finite and $f$ is finite on X a.e then $\lim_{n\to \infty}\mu \{x: |f(x)|\geq n\}=0$

Number of equivalence classes of functions of real variable with the a.e relation.

Is the completion of a measure space necessary?

Showing a certain function vanishes almost everywhere

$\mu(A \cap I) \le a \mu(I)$ implies $\mu(A) = 0$?

Showing continuous functions are dense in $L^p([0,1],\lambda)$, where $\lambda$ is Lebesgue measure

Borel measure induced by the Cantor function?

existence of a sequence of continuous functions with two conditions

Find the limit $\lim \int_{(0,1]} f_n \, d\lambda $ where $ \lambda $ is lebesgue measure

Lebsegue measure of $\{ 0<x \leq 1: x \sin \left(\frac{\pi}{2x}\right) \geq 0 \}$

Properties of decreasing sequence of Lebesgue measurable sets.

L'Hôpital with absolute continuity

Repeated extension of Lebesgue measure

Property of a set of a positive Lebesgue measure

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