Question

Example of a sequence of integrable functions on $[0,1]$ s.t. $\lim_{n\to\infty}\int_0^1|f_n(x)|\,dx = 0$ but $f_n$ not converges to $0$ a.e?

score 116 · Answer 1 · 2026-04-15 16:10:02

116

Views

Example of a sequence of integrable functions on $[0,1]$ s.t. $\lim_{n\to\infty}\int_0^1|f_n(x)|\,dx = 0$ but $f_n$ not converges to $0$ a.e?

Published on 15 Apr 2026 - 16:10

score 144 · Answer 2 · 2026-04-15 19:12:14

144

Views

Lebesgue measure: $\lim_{t\to 0} m((B+t)\cap B)=m(B) $?

Published on 15 Apr 2026 - 19:12

score 89 · Answer 3 · 2026-04-16 16:57:45

89

Views

Lebesgue integral $\int 0d\mu=0?$ How to compute it?

Published on 16 Apr 2026 - 16:57

score 579 · Answer 4 · 2026-04-13 20:58:45

579

Views

Product Spaces and Integrals of Indicator Functions

Published on 13 Apr 2026 - 20:58

score 262 · Answer 5 · 2026-04-17 11:42:18

262

Views

$\lim_{n\to\infty}\int_{\Omega}|f_n - f|dx = 0$, if $\forall \epsilon > 0, \exists N | \forall n,m > N, \int_{\Omega}|f_n - f_m|dx < \epsilon$.

Published on 17 Apr 2026 - 11:42

score 1k · Answer 6 · 2026-04-12 05:35:28

1k

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Breaking up domain of integration for a Lebesgue Integral

Published on 12 Apr 2026 - 5:35

score 58 · Answer 7 · 2026-04-10 16:22:49

58

Views

Is the following function integrable?

Published on 10 Apr 2026 - 16:22

score 248 · Answer 8 · 2026-04-13 16:59:14

248

Views

Calculate integral for every Lebesgue point of a function $f \in L^1(-\infty, \infty)$

Published on 13 Apr 2026 - 16:59

score 131 · Answer 9 · 2026-04-14 15:13:30

131

Views

Example of functions where limit and integral are interchangeable on $\mathbb R$ but not on a measurable subset

Published on 14 Apr 2026 - 15:13

score 989 · Answer 10 · 2026-04-11 11:33:26

989

Views

Well-definedness of Lebesgue-Integral for non-negative measurable functions

Published on 11 Apr 2026 - 11:33

score 315 · Answer 11 · 2026-04-10 02:21:34

315

Views

Is my function Lebesgue integrable but not Riemann?

Published on 10 Apr 2026 - 2:21

score 156 · Answer 12 · 2026-04-11 20:18:25

156

Views

Dominated Convergence Theorem to Evaluate Integral

Published on 11 Apr 2026 - 20:18

score 470 · Answer 13 · 2026-04-15 00:23:57

470

Views

Another way of showing that $\int_0^{\infty}\frac{\sin x}{x}dx = \frac{\pi}{2}$

Published on 15 Apr 2026 - 0:23

score 171 · Answer 14 · 2026-03-27 02:50:54

171

Views

Integration by parts to prove a function is constant a.e.

Published on 27 Mar 2026 - 2:50

score 819 · Answer 15 · 2026-04-29 19:13:45

819

Views

Function between two measurable functions is measurable

Published on 29 Apr 2026 - 19:13

List Question

Example of a sequence of integrable functions on $[0,1]$ s.t. $\lim_{n\to\infty}\int_0^1|f_n(x)|\,dx = 0$ but $f_n$ not converges to $0$ a.e?

Lebesgue measure: $\lim_{t\to 0} m((B+t)\cap B)=m(B) $?

Lebesgue integral $\int 0d\mu=0?$ How to compute it?

Product Spaces and Integrals of Indicator Functions

$\lim_{n\to\infty}\int_{\Omega}|f_n - f|dx = 0$, if $\forall \epsilon > 0, \exists N | \forall n,m > N, \int_{\Omega}|f_n - f_m|dx < \epsilon$.

Breaking up domain of integration for a Lebesgue Integral

Is the following function integrable?

Calculate integral for every Lebesgue point of a function $f \in L^1(-\infty, \infty)$

Example of functions where limit and integral are interchangeable on $\mathbb R$ but not on a measurable subset

Well-definedness of Lebesgue-Integral for non-negative measurable functions

Is my function Lebesgue integrable but not Riemann?

Dominated Convergence Theorem to Evaluate Integral

Another way of showing that $\int_0^{\infty}\frac{\sin x}{x}dx = \frac{\pi}{2}$

Integration by parts to prove a function is constant a.e.

Function between two measurable functions is measurable

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