Question

Let $(X,M,\mu)$ be a measure space and let $ f:X \to R$ be a measurable function.Prove that the positive measure $\mu$ is finite

score 625 · Answer 1 · 2026-04-16 03:59:57

Let $(X,M,\mu)$ be a measure space and let $ f:X \to R$ be a measurable function.Prove that the positive measure $\mu$ is finite

score 144 · Answer 2 · 2026-04-09 13:35:14

144

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Any Sequence of a Measurable Sets Has a Convergent Subsequence?

Published on 09 Apr 2026 - 13:35

score 101 · Answer 3 · 2026-04-16 05:08:32

101

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Does there exists a $\mathbb{Q}$ vector space automorphism of $\mathbb{R}$ which is not Lebesgue measurable?

Published on 16 Apr 2026 - 5:08

score 1.3k · Answer 4 · 2026-04-13 12:30:56

1.3k

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Homeomorphism of Borel set is Borel

Published on 13 Apr 2026 - 12:30

score 183 · Answer 5 · 2026-04-17 11:22:54

183

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What is the point of having continuity from below and above?

Published on 17 Apr 2026 - 11:22

score 657 · Answer 6 · 2026-04-16 05:31:02

657

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Prove $\mathcal{F}$ is a $\sigma$-algebra if and only if it satisfies the following condition

Published on 16 Apr 2026 - 5:31

score 141 · Answer 7 · 2026-04-14 01:12:49

141

Views

If $\int_Af_nd\mu\to\int_A fd\mu$ for all $A$, what type of convergence $f_n\to f$ do we have?

Published on 14 Apr 2026 - 1:12

score 166 · Answer 8 · 2026-04-14 14:17:02

166

Views

On Riemann integral

Published on 14 Apr 2026 - 14:17

score 46 · Answer 9 · 2026-04-14 13:12:21

46

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Sigma-algebra defined by intersection

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score 31 · Answer 10 · 2026-04-13 20:31:00

31

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Sets in a ring that are subset of another set in the ring

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score 579 · Answer 11 · 2026-04-14 05:24:05

579

Views

Borel sigma algebra on the set of cont. functions

Published on 14 Apr 2026 - 5:24

score 1.9k · Answer 12 · 2026-04-11 11:43:07

1.9k

Views

How to prove every open set is Lebesgue measurable?

Published on 11 Apr 2026 - 11:43

score 75 · Answer 13 · 2026-04-09 22:02:49

75

Views

Integration over level sets

Published on 09 Apr 2026 - 22:02

score 537 · Answer 14 · 2026-04-15 15:19:28

537

Views

Two probability measures $P,Q$ which do not admit densities wrt Lebesgue measure but have computable $\frac{dP}{dQ}$?

Published on 15 Apr 2026 - 15:19

score 103 · Answer 15 · 2026-04-15 06:06:57

103

Views

Why do we need a finite measure to have this theorem?

Published on 15 Apr 2026 - 6:06

List Question

Let $(X,M,\mu)$ be a measure space and let $ f:X \to R$ be a measurable function.Prove that the positive measure $\mu$ is finite

Any Sequence of a Measurable Sets Has a Convergent Subsequence?

Does there exists a $\mathbb{Q}$ vector space automorphism of $\mathbb{R}$ which is not Lebesgue measurable?

Homeomorphism of Borel set is Borel

What is the point of having continuity from below and above?

Prove $\mathcal{F}$ is a $\sigma$-algebra if and only if it satisfies the following condition

If $\int_Af_nd\mu\to\int_A fd\mu$ for all $A$, what type of convergence $f_n\to f$ do we have?

On Riemann integral

Sigma-algebra defined by intersection

Sets in a ring that are subset of another set in the ring

Borel sigma algebra on the set of cont. functions

How to prove every open set is Lebesgue measurable?

Integration over level sets

Two probability measures $P,Q$ which do not admit densities wrt Lebesgue measure but have computable $\frac{dP}{dQ}$?

Why do we need a finite measure to have this theorem?

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