Question

Is $\lim_{h \to 0} \int_0^h |f(x+h)-f(x)| dx = 0$?

score 163 · Answer 1 · 2026-04-10 10:02:40

163

Views

Is $\lim_{h \to 0} \int_0^h |f(x+h)-f(x)| dx = 0$?

Published on 10 Apr 2026 - 10:02

score 77 · Answer 2 · 2026-04-16 15:15:38

77

Views

Fourier coefficients of $\chi_E$ assuming $m(E)=1.$

Published on 16 Apr 2026 - 15:15

score 172 · Answer 3 · 2026-04-12 05:50:50

172

Views

Computing limit using Dominated Convergence Theorem

Published on 12 Apr 2026 - 5:50

score 195 · Answer 4 · 2026-04-15 20:31:28

195

Views

For $f :\mathbb{R} \rightarrow \mathbb{R}\displaystyle$ we have ${\lim_{n \to +\infty} f(x+n) =0}$ almost everywhere

Published on 15 Apr 2026 - 20:31

score 173 · Answer 5 · 2026-04-15 12:05:33

173

Views

Automorphism on the unit interval compatible with a measure preserving set function

Published on 15 Apr 2026 - 12:05

score 340 · Answer 6 · 2026-04-17 06:39:05

340

Views

Union of Balls around Rationals

Published on 17 Apr 2026 - 6:39

score 86 · Answer 7 · 2026-04-16 23:19:37

86

Views

Prove that $f$ is integrable given that f is a positive measurable function on [0,1]

Published on 16 Apr 2026 - 23:19

score 717 · Answer 8 · 2026-04-18 14:27:11

717

Views

Find the Lebesgue measure of simplex $\{(x_1, x_2, ... ,x_d)\in \mathbb R^d : 0 < x_1 < x_2 < ... < x_d < 1\}$

Published on 18 Apr 2026 - 14:27

score 109 · Answer 9 · 2026-04-12 03:16:08

109

Views

Proving an inequality in 3 dimensional standard Lebesgue measure and geometrical interpretation

Published on 12 Apr 2026 - 3:16

score 237 · Answer 10 · 2026-04-07 23:18:22

237

Views

$L^p$ space: For $1≤p≤∞$, find the values of the parameter $λ$ for which $\lim$ (integral) $= 0$

Published on 07 Apr 2026 - 23:18

score 1k · Answer 11 · 2026-04-17 01:59:30

1k

Views

Integral of a shifted function

Published on 17 Apr 2026 - 1:59

score 51 · Answer 12 · 2026-04-13 05:15:45

51

Views

Proving H. Steinhaus with the continuity of the function $\overline{\lambda}_{A,B}$

Published on 13 Apr 2026 - 5:15

score 28 · Answer 13 · 2026-04-16 01:52:06

28

Views

Show that $\int _X f \:\:d\mu$ is NOT dependent on the representation of the simple function $f$

Published on 16 Apr 2026 - 1:52

score 773 · Answer 14 · 2026-04-11 06:50:53

773

Views

How can I prove a function on product space lebesgue measurable?

Published on 11 Apr 2026 - 6:50

score 40 · Answer 15 · 2026-04-13 09:30:21

40

Views

Identity involving two related measures

Published on 13 Apr 2026 - 9:30

List Question

Is $\lim_{h \to 0} \int_0^h |f(x+h)-f(x)| dx = 0$?

Fourier coefficients of $\chi_E$ assuming $m(E)=1.$

Computing limit using Dominated Convergence Theorem

For $f :\mathbb{R} \rightarrow \mathbb{R}\displaystyle$ we have ${\lim_{n \to +\infty} f(x+n) =0}$ almost everywhere

Automorphism on the unit interval compatible with a measure preserving set function

Union of Balls around Rationals

Prove that $f$ is integrable given that f is a positive measurable function on [0,1]

Find the Lebesgue measure of simplex $\{(x_1, x_2, ... ,x_d)\in \mathbb R^d : 0 < x_1 < x_2 < ... < x_d < 1\}$

Proving an inequality in 3 dimensional standard Lebesgue measure and geometrical interpretation

$L^p$ space: For $1≤p≤∞$, find the values of the parameter $λ$ for which $\lim$ (integral) $= 0$

Integral of a shifted function

Proving H. Steinhaus with the continuity of the function $\overline{\lambda}_{A,B}$

Show that $\int _X f \:\:d\mu$ is NOT dependent on the representation of the simple function $f$

How can I prove a function on product space lebesgue measurable?

Identity involving two related measures

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