Question

Prove under finite measure equivalent statements

score 85 · Answer 1 · 2026-04-14 15:28:41

85

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Prove under finite measure equivalent statements

Published on 14 Apr 2026 - 15:28

score 1.2k · Answer 2 · 2026-04-14 12:38:25

1.2k

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Why is the undergraph definition of Lebesgue integral so rare?

Published on 14 Apr 2026 - 12:38

score 471 · Answer 3 · 2026-04-28 20:17:35

471

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Proving a few things about $ L^{p} $-spaces

Published on 28 Apr 2026 - 20:17

score 467 · Answer 4 · 2026-04-28 20:23:10

467

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Suppose $\{f_k\}$ is a sequence of $M$-measurable functions on $X$. Let $p_1$ and $p_2\in [1,\infty)$, and suppose $f_k\in L^{p_1}\cap L^{p_2}$.

Published on 28 Apr 2026 - 20:23

score 234 · Answer 5 · 2026-04-28 20:23:20

234

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Find an example of a sequence $\{f_k\}$ such that $f_k\in L^p$ for $1\le p <\infty$, $f_k\to0$ in $L^p$ for $1\le p < p_0$

Published on 28 Apr 2026 - 20:23

score 5.3k · Answer 6 · 2026-04-28 20:20:27

5.3k

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Properties of $||f||_{\infty}$ - the infinity norm

Published on 28 Apr 2026 - 20:20

score 168 · Answer 7 · 2026-04-16 11:27:21

168

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Show a set is in Borel sigma algebra

Published on 16 Apr 2026 - 11:27

score 132 · Answer 8 · 2026-04-11 00:08:16

132

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Does showing a function is integrable suffice to show the function is measurable?

Published on 11 Apr 2026 - 0:08

score 1.4k · Answer 9 · 2026-04-13 11:28:53

1.4k

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On why the Vitali Covering Lemma does not apply when the covering collection contains degenerate closed intervals

Published on 13 Apr 2026 - 11:28

score 266 · Answer 10 · 2026-04-12 03:45:00

266

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step function vs integrable function

Published on 12 Apr 2026 - 3:45

score 124 · Answer 11 · 2026-04-16 21:19:36

124

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Give an example of $f\in L^1$, $g\in L^{\infty}$, such that $fg\notin C_0$ (meaning $\lim_{|x|\to\infty}(fg)(x)\neq0$)

Published on 16 Apr 2026 - 21:19

score 186 · Answer 12 · 2026-04-28 21:44:41

186

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convergence on $L^p$ space

Published on 28 Apr 2026 - 21:44

score 5.3k · Answer 13 · 2026-04-15 20:35:28

5.3k

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$L^2$ function on finite interval implies $L^1$?

Published on 15 Apr 2026 - 20:35

score 1.8k · Answer 14 · 2026-04-11 19:20:13

1.8k

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Are integrable, essentially bounded functions in L^p?

Published on 11 Apr 2026 - 19:20

score 2.4k · Answer 15 · 2026-04-12 19:58:55

2.4k

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Need help badly: n-dimensional Lebesgue measure of a hyperplane is zero.

Published on 12 Apr 2026 - 19:58

List Question

Prove under finite measure equivalent statements

Why is the undergraph definition of Lebesgue integral so rare?

Proving a few things about $ L^{p} $-spaces

Suppose $\{f_k\}$ is a sequence of $M$-measurable functions on $X$. Let $p_1$ and $p_2\in [1,\infty)$, and suppose $f_k\in L^{p_1}\cap L^{p_2}$.

Find an example of a sequence $\{f_k\}$ such that $f_k\in L^p$ for $1\le p <\infty$, $f_k\to0$ in $L^p$ for $1\le p < p_0$

Properties of $||f||_{\infty}$ - the infinity norm

Show a set is in Borel sigma algebra

Does showing a function is integrable suffice to show the function is measurable?

On why the Vitali Covering Lemma does not apply when the covering collection contains degenerate closed intervals

step function vs integrable function

Give an example of $f\in L^1$, $g\in L^{\infty}$, such that $fg\notin C_0$ (meaning $\lim_{|x|\to\infty}(fg)(x)\neq0$)

convergence on $L^p$ space

$L^2$ function on finite interval implies $L^1$?

Are integrable, essentially bounded functions in L^p?

Need help badly: n-dimensional Lebesgue measure of a hyperplane is zero.

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