Question

Sequence $f_n$ bounded in $L^1$ such that $\int_0^x f_n\to \int_0^x f$ for all $x,$ but such that ...

score 198 · Answer 1 · 2026-04-15 16:54:11

198

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Sequence $f_n$ bounded in $L^1$ such that $\int_0^x f_n\to \int_0^x f$ for all $x,$ but such that ...

Published on 15 Apr 2026 - 16:54

score 42 · Answer 2 · 2026-04-13 23:24:32

42

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Is there a $\mathbb{L}^{1}(\mathbb(0,1))$ bound for $\sum_{n=1}^{\infty}\frac{\ln(x)}{(n(nx²+1))}$

Published on 13 Apr 2026 - 23:24

score 244 · Answer 3 · 2026-05-11 06:15:33

244

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Approximate a simple function with the sum of two simple functions

Published on 11 May 2026 - 6:15

score 109 · Answer 4 · 2026-04-09 00:19:16

109

Views

Extending bounded convergence theorem

Published on 09 Apr 2026 - 0:19

score 54 · Answer 5 · 2026-04-26 00:41:41

54

Views

How $\boldsymbol 1_{\mathbb Q\cap [-2,2]}$ can be more regular that $\boldsymbol 1_{[0,1]}$?

Published on 26 Apr 2026 - 0:41

score 142 · Answer 6 · 2026-04-14 04:08:13

142

Views

show that $f = c$ a.e.

Published on 14 Apr 2026 - 4:08

score 136 · Answer 7 · 2026-04-17 07:37:49

136

Views

pointwise convergence of mollification combined with a cut-off function

Published on 17 Apr 2026 - 7:37

score 1.8k · Answer 8 · 2026-04-10 23:13:31

1.8k

Views

Is product of Lebesgue integrable functions also Lebesgue integrable

Published on 10 Apr 2026 - 23:13

score 1.6k · Answer 9 · 2026-04-11 10:24:05

1.6k

Views

definition of measurability of extended real value function

Published on 11 Apr 2026 - 10:24

score 194 · Answer 10 · 2026-05-11 09:04:21

194

Views

How to compute the integral on product measure

Published on 11 May 2026 - 9:04

score 276 · Answer 11 · 2026-04-12 14:06:56

276

Views

Uniformly integrable random variables remain uniformly integrable after centering

Published on 12 Apr 2026 - 14:06

score 98 · Answer 12 · 2026-04-29 14:22:48

98

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How can I prove that $\mu(\{0\}) \neq 0$?

Published on 29 Apr 2026 - 14:22

score 175 · Answer 13 · 2026-04-10 17:14:19

175

Views

metric on Positive Borel measures and absolutely continuity w.r.t to Lebesgue measure.

Published on 10 Apr 2026 - 17:14

score 361 · Answer 14 · 2026-04-12 10:42:42

361

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Question in the proof of Lebesgue's Dominated Convergence Theorem

Published on 12 Apr 2026 - 10:42

score 2.2k · Answer 15 · 2026-04-16 16:17:36

2.2k

Views

Prove that the two measures are the same

Published on 16 Apr 2026 - 16:17

List Question

Sequence $f_n$ bounded in $L^1$ such that $\int_0^x f_n\to \int_0^x f$ for all $x,$ but such that ...

Is there a $\mathbb{L}^{1}(\mathbb(0,1))$ bound for $\sum_{n=1}^{\infty}\frac{\ln(x)}{(n(nx²+1))}$

Approximate a simple function with the sum of two simple functions

Extending bounded convergence theorem

How $\boldsymbol 1_{\mathbb Q\cap [-2,2]}$ can be more regular that $\boldsymbol 1_{[0,1]}$?

show that $f = c$ a.e.

pointwise convergence of mollification combined with a cut-off function

Is product of Lebesgue integrable functions also Lebesgue integrable

definition of measurability of extended real value function

How to compute the integral on product measure

Uniformly integrable random variables remain uniformly integrable after centering

How can I prove that $\mu(\{0\}) \neq 0$?

metric on Positive Borel measures and absolutely continuity w.r.t to Lebesgue measure.

Question in the proof of Lebesgue's Dominated Convergence Theorem

Prove that the two measures are the same

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