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Question about James Munkres's "Analysis on Manifolds", p.112, Theorem 14.1

score 157 · Answer 1 · 2026-04-14 17:45:14

157

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Question about James Munkres's "Analysis on Manifolds", p.112, Theorem 14.1

Published on 14 Apr 2026 - 17:45

score 49 · Answer 2 · 2026-04-16 11:15:23

49

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Give an example function $f \in L_p(\mathbb {R}) \forall \: p > 7,$ but $f \notin L_p(\mathbb {R}) \: p \leq 7$

Published on 16 Apr 2026 - 11:15

score 34 · Answer 3 · 2026-04-15 13:24:12

34

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If F is closed show F is Lebesgue measurable

Published on 15 Apr 2026 - 13:24

score 621 · Answer 4 · 2026-04-17 10:58:44

621

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Construction of open set dense in $[0,1]$ with measure $\varepsilon$

Published on 17 Apr 2026 - 10:58

score 30 · Answer 5 · 2026-04-16 07:40:52

30

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Can we say that there exists $j_0>1$ such that $\{M_j\}_{j\geq j_0}$ is non-increasing sequence?

Published on 16 Apr 2026 - 7:40

score 943 · Answer 6 · 2026-04-15 22:44:36

943

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For (Lebesgue) measurable functions $f$ and $g$, if $f=g$ a.e., then $ \int_{E} f=\int_{E} g. $

Published on 15 Apr 2026 - 22:44

score 97 · Answer 7 · 2026-03-26 23:09:31

97

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Simple Change of Variables in Lebesgue Integration

Published on 26 Mar 2026 - 23:09

score 481 · Answer 8 · 2026-04-16 10:51:53

481

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Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$

Published on 16 Apr 2026 - 10:51

score 201 · Answer 9 · 2026-04-16 04:06:14

201

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Set of lower dimension has Lebesgue measure zero?

Published on 16 Apr 2026 - 4:06

score 617 · Answer 10 · 2026-04-10 07:31:43

617

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Proving $E$ is measurable iff $E^C$ measurable... using the alternative definition

Published on 10 Apr 2026 - 7:31

score 346 · Answer 11 · 2026-04-16 02:53:50

346

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Proving that Caratheodory's Criterion holds..... but How to Make it Precise?

Published on 16 Apr 2026 - 2:53

score 66 · Answer 12 · 2026-04-12 09:19:10

66

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Lebesgue measure of a certain subset in $\mathbb{R}^2$

Published on 12 Apr 2026 - 9:19

score 1k · Answer 13 · 2026-04-09 21:19:11

1k

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Radon-Nikodym Derivative of a Mixed Distribution

Published on 09 Apr 2026 - 21:19

score 121 · Answer 14 · 2026-04-13 00:17:52

121

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The boundary of a disc has zero measure

Published on 13 Apr 2026 - 0:17

score 30 · Answer 15 · 2026-04-09 14:08:41

30

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Lebesgue measure/integral problem - where do I go wrong?

Published on 09 Apr 2026 - 14:08

List Question

Question about James Munkres's "Analysis on Manifolds", p.112, Theorem 14.1

Give an example function $f \in L_p(\mathbb {R}) \forall \: p > 7,$ but $f \notin L_p(\mathbb {R}) \: p \leq 7$

If F is closed show F is Lebesgue measurable

Construction of open set dense in $[0,1]$ with measure $\varepsilon$

Can we say that there exists $j_0>1$ such that $\{M_j\}_{j\geq j_0}$ is non-increasing sequence?

For (Lebesgue) measurable functions $f$ and $g$, if $f=g$ a.e., then $ \int_{E} f=\int_{E} g. $

Simple Change of Variables in Lebesgue Integration

Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$

Set of lower dimension has Lebesgue measure zero?

Proving $E$ is measurable iff $E^C$ measurable... using the alternative definition

Proving that Caratheodory's Criterion holds..... but How to Make it Precise?

Lebesgue measure of a certain subset in $\mathbb{R}^2$

Radon-Nikodym Derivative of a Mixed Distribution

The boundary of a disc has zero measure

Lebesgue measure/integral problem - where do I go wrong?

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