Question

Function $L^1_{\mathrm{loc}}(\mathbb{R})$

score 241 · Answer 1 · 2026-04-16 03:51:18

241

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Function $L^1_{\mathrm{loc}}(\mathbb{R})$

Published on 16 Apr 2026 - 3:51

score 71 · Answer 2 · 2026-04-10 22:47:31

71

Views

Integrability of a square of an integral

Published on 10 Apr 2026 - 22:47

score 85 · Answer 3 · 2026-04-15 13:32:28

85

Views

Solve integral: $\int_{0}^{\pi}\sum_{k=1}^{\infty}(\frac{k^2\sin{kx}}{2^k})dx$

Published on 15 Apr 2026 - 13:32

score 1.1k · Answer 4 · 2026-04-12 18:35:39

1.1k

Views

Physical interpretation of Lebesgue norm $L^p$

Published on 12 Apr 2026 - 18:35

score 257 · Answer 5 · 2026-04-16 14:10:56

257

Views

How to prove that, $\lim\limits_{k \rightarrow \infty} \int_{\Bbb{R}} f_k(x) g(x) dm(x) = 0$

Published on 16 Apr 2026 - 14:10

score 31 · Answer 6 · 2026-04-30 02:59:28

31

Views

Proving that the limit of an $L^p$ sequence is also $L^p$

Published on 30 Apr 2026 - 2:59

score 123 · Answer 7 · 2026-04-14 04:09:55

123

Views

Monotone Convergence Theorem for sets of functions instead of sequences

Published on 14 Apr 2026 - 4:09

score 199 · Answer 8 · 2026-04-16 14:41:49

199

Views

Weak convergence, $\displaystyle f\in L^p(\Bbb R^d) $ and $g\in L^q(\Bbb R^d) $ then, $\lim_{j\to\infty} \int_{\Bbb R^d}f_j(x)g(x)dx = 0$

Published on 16 Apr 2026 - 14:41

score 118 · Answer 9 · 2026-04-12 10:40:49

118

Views

Is a non-negative, Lebesgue-measurable function with finite integral equal to $\infty$ on at most a set of measure zero?

Published on 12 Apr 2026 - 10:40

score 70 · Answer 10 · 2026-04-13 18:09:36

70

Views

Increasing, $\mu$-a.e. point-wise convergent sequence of positive $\mu$-integrable functions is cauchy sequence

Published on 13 Apr 2026 - 18:09

score 1.4k · Answer 11 · 2026-04-16 07:36:54

1.4k

Views

$\int_{\Bbb R ^2} e^{-x^2-y^2} \, dx \, dy$

Published on 16 Apr 2026 - 7:36

score 677 · Answer 12 · 2026-04-16 04:25:29

677

Views

If $f\in L^1(\Bbb R,dx)$ then prove that for almost every $x\in\Bbb R$ $\lim\limits_{n\to \infty} f(nx) = 0.$

Published on 16 Apr 2026 - 4:25

score 364 · Answer 13 · 2026-04-11 21:24:20

364

Views

A counterexample to Fubini

Published on 11 Apr 2026 - 21:24

score 217 · Answer 14 · 2026-04-16 04:01:24

217

Views

Determine if $\lim_{n\rightarrow \infty }\int_{-\infty}^{\infty}\frac{(\sin(x))^{n}}{x^2+1}d\lambda(x)$ exists and calculate its value if it exists.

Published on 16 Apr 2026 - 4:01

score 285 · Answer 15 · 2026-04-12 20:25:09

285

Views

Limit of lebesgue-integrable functions

Published on 12 Apr 2026 - 20:25

List Question

Function $L^1_{\mathrm{loc}}(\mathbb{R})$

Integrability of a square of an integral

Solve integral: $\int_{0}^{\pi}\sum_{k=1}^{\infty}(\frac{k^2\sin{kx}}{2^k})dx$

Physical interpretation of Lebesgue norm $L^p$

How to prove that, $\lim\limits_{k \rightarrow \infty} \int_{\Bbb{R}} f_k(x) g(x) dm(x) = 0$

Proving that the limit of an $L^p$ sequence is also $L^p$

Monotone Convergence Theorem for sets of functions instead of sequences

Weak convergence, $\displaystyle f\in L^p(\Bbb R^d) $ and $g\in L^q(\Bbb R^d) $ then, $\lim_{j\to\infty} \int_{\Bbb R^d}f_j(x)g(x)dx = 0$

Is a non-negative, Lebesgue-measurable function with finite integral equal to $\infty$ on at most a set of measure zero?

Increasing, $\mu$-a.e. point-wise convergent sequence of positive $\mu$-integrable functions is cauchy sequence

$\int_{\Bbb R ^2} e^{-x^2-y^2} \, dx \, dy$

If $f\in L^1(\Bbb R,dx)$ then prove that for almost every $x\in\Bbb R$ $\lim\limits_{n\to \infty} f(nx) = 0.$

A counterexample to Fubini

Determine if $\lim_{n\rightarrow \infty }\int_{-\infty}^{\infty}\frac{(\sin(x))^{n}}{x^2+1}d\lambda(x)$ exists and calculate its value if it exists.

Limit of lebesgue-integrable functions

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