Question

continuous real-valued functions $f=g$ $\lambda$-a.e. ($\lambda$ is the Lebesgue measure) implies $f=g$ everywhere

score 212 · Answer 1 · 2026-04-10 17:23:25

212

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continuous real-valued functions $f=g$ $\lambda$-a.e. ($\lambda$ is the Lebesgue measure) implies $f=g$ everywhere

Published on 10 Apr 2026 - 17:23

score 598 · Answer 2 · 2026-04-27 19:47:06

598

Views

Show that $f$ is integrable $\implies $ $f$ finite a.e.

Published on 27 Apr 2026 - 19:47

score 131 · Answer 3 · 2026-04-27 19:48:03

131

Views

Proof that $\lim_{n\to\infty}\int_S\ f^{1/n} \, dm = m(S)$

Published on 27 Apr 2026 - 19:48

score 88 · Answer 4 · 2026-04-15 04:14:19

88

Views

Aproximation of outer-measurable sets

Published on 15 Apr 2026 - 4:14

score 132 · Answer 5 · 2026-04-27 19:46:31

132

Views

Prove that lebesgue integrable equal lebesgue measure

Published on 27 Apr 2026 - 19:46

score 86 · Answer 6 · 2026-04-11 15:29:23

86

Views

A trivial invariant by translations measure

Published on 11 Apr 2026 - 15:29

score 182 · Answer 7 · 2026-04-16 03:43:15

182

Views

Cardinality of preimage(inverse image), relation to Lebesgue integral and total variation

Published on 16 Apr 2026 - 3:43

score 98 · Answer 8 · 2026-04-09 23:40:34

98

Views

Reflection about Gaussian measures

Published on 09 Apr 2026 - 23:40

score 3.7k · Answer 9 · 2026-04-14 07:34:52

3.7k

Views

Dominated convergence theorem and uniformly convergence

Published on 14 Apr 2026 - 7:34

score 1k · Answer 10 · 2026-04-11 19:11:31

1k

Views

Prove composition is a measurable function

Published on 11 Apr 2026 - 19:11

score 1k · Answer 11 · 2026-04-11 20:28:32

1k

Views

Problem in understanding the proof of Lebesgue-Radon-Nikodym Theorem

Published on 11 Apr 2026 - 20:28

score 177 · Answer 12 · 2026-04-27 21:05:49

177

Views

Question for dominated convergence theorem.

Published on 27 Apr 2026 - 21:05

score 611 · Answer 13 · 2026-04-27 21:07:06

611

Views

Represent total variation of continuous function by integration of counting function

Published on 27 Apr 2026 - 21:07

score 141 · Answer 14 · 2026-04-13 05:27:23

141

Views

Condition for $\mu^*$-measurable set

Published on 13 Apr 2026 - 5:27

score 84 · Answer 15 · 2026-04-27 21:10:04

84

Views

If $f$ is non negative measurable, $ \int f \lt \infty $ if and only if $\sum_{n=-\infty}^{\infty} 2^{n} m{(f\gt 2^n)} \lt\infty $

Published on 27 Apr 2026 - 21:10

List Question

continuous real-valued functions $f=g$ $\lambda$-a.e. ($\lambda$ is the Lebesgue measure) implies $f=g$ everywhere

Show that $f$ is integrable $\implies $ $f$ finite a.e.

Proof that $\lim_{n\to\infty}\int_S\ f^{1/n} \, dm = m(S)$

Aproximation of outer-measurable sets

Prove that lebesgue integrable equal lebesgue measure

A trivial invariant by translations measure

Cardinality of preimage(inverse image), relation to Lebesgue integral and total variation

Reflection about Gaussian measures

Dominated convergence theorem and uniformly convergence

Prove composition is a measurable function

Problem in understanding the proof of Lebesgue-Radon-Nikodym Theorem

Question for dominated convergence theorem.

Represent total variation of continuous function by integration of counting function

Condition for $\mu^*$-measurable set

If $f$ is non negative measurable, $ \int f \lt \infty $ if and only if $\sum_{n=-\infty}^{\infty} 2^{n} m{(f\gt 2^n)} \lt\infty $

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