Question

What can we tell about a sequence of measurable functions on a finite measure space such that $\sup_n \int_X |f_n(x)|^2 d\mu < \infty$?

score 284 · Answer 1 · 2026-04-16 11:10:08

284

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What can we tell about a sequence of measurable functions on a finite measure space such that $\sup_n \int_X |f_n(x)|^2 d\mu < \infty$?

Published on 16 Apr 2026 - 11:10

score 4.3k · Answer 2 · 2026-04-16 09:49:54

4.3k

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$f(x)=1/x$ over $[1, \infty)$ is not Lebesgue integrable

Published on 16 Apr 2026 - 9:49

score 6k · Answer 3 · 2026-04-13 21:27:25

6k

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Integration by parts and Lebesgue-Stieltjes integrals

Published on 13 Apr 2026 - 21:27

score 268 · Answer 4 · 2026-04-11 18:46:10

268

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Uniform integrability and Lebesgue convergence

Published on 11 Apr 2026 - 18:46

score 228 · Answer 5 · 2026-04-13 02:24:13

228

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using sup of an unbounded function

Published on 13 Apr 2026 - 2:24

score 3.2k · Answer 6 · 2026-04-14 19:45:36

3.2k

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Lebesgue Integral on a set of measure zero

Published on 14 Apr 2026 - 19:45

score 850 · Answer 7 · 2026-04-12 08:45:06

850

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Extension of Fatou's lemma

Published on 12 Apr 2026 - 8:45

score 21.4k · Answer 8 · 2026-04-14 05:54:21

21.4k

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Showing that $1/x$ is NOT Lebesgue Integrable on $(0,1]$

Published on 14 Apr 2026 - 5:54

score 137 · Answer 9 · 2026-04-15 09:44:27

137

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$\lim_{n \to \infty} \int^n_{-n}fdm=\int fdm$

Published on 15 Apr 2026 - 9:44

score 3.5k · Answer 10 · 2026-04-12 07:03:34

3.5k

Views

Finding Lebesgue Integral of $\frac{1}{\sqrt{x}}$ over $(0,1]$

Published on 12 Apr 2026 - 7:03

score 161 · Answer 11 · 2026-04-11 08:48:28

161

Views

Limit and Lebesgue integral in a compact

Published on 11 Apr 2026 - 8:48

score 1.1k · Answer 12 · 2026-04-17 00:52:23

1.1k

Views

Trying to show that a function is zero almost everywhere given a constraint on its Lebesgue measure.

Published on 17 Apr 2026 - 0:52

score 673 · Answer 13 · 2026-04-11 04:40:34

673

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Limit of a measurable function and the Lebesgue integral

Published on 11 Apr 2026 - 4:40

score 106 · Answer 14 · 2026-04-15 06:47:29

106

Views

Uniform integrablity of measurable functions

Published on 15 Apr 2026 - 6:47

score 4.5k · Answer 15 · 2026-04-13 18:11:42

4.5k

Views

{$\int_{[1/n,1]}f$} to converge and yet $f$ is not $L$-integrable over $[0,1]$

Published on 13 Apr 2026 - 18:11

List Question

What can we tell about a sequence of measurable functions on a finite measure space such that $\sup_n \int_X |f_n(x)|^2 d\mu < \infty$?

$f(x)=1/x$ over $[1, \infty)$ is not Lebesgue integrable

Integration by parts and Lebesgue-Stieltjes integrals

Uniform integrability and Lebesgue convergence

using sup of an unbounded function

Lebesgue Integral on a set of measure zero

Extension of Fatou's lemma

Showing that $1/x$ is NOT Lebesgue Integrable on $(0,1]$

$\lim_{n \to \infty} \int^n_{-n}fdm=\int fdm$

Finding Lebesgue Integral of $\frac{1}{\sqrt{x}}$ over $(0,1]$

Limit and Lebesgue integral in a compact

Trying to show that a function is zero almost everywhere given a constraint on its Lebesgue measure.

Limit of a measurable function and the Lebesgue integral

Uniform integrablity of measurable functions

{$\int_{[1/n,1]}f$} to converge and yet $f$ is not $L$-integrable over $[0,1]$

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