Question

Showing that if A$\subset$E$\subset$B and lebesgue measures of A and B are equal and finite, then E is lebesgue measurable.

score 919 · Answer 1 · 2026-04-15 07:31:51

919

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Showing that if A$\subset$E$\subset$B and lebesgue measures of A and B are equal and finite, then E is lebesgue measurable.

Published on 15 Apr 2026 - 7:31

score 154 · Answer 2 · 2026-04-14 10:36:05

154

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A lebesgue measurable set $E$ with $\mu(E)=1$ and $\mu_F(E) = 0$.

Published on 14 Apr 2026 - 10:36

score 126 · Answer 3 · 2026-04-11 20:05:15

126

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Definition of the Lebesgue integral

Published on 11 Apr 2026 - 20:05

score 42 · Answer 4 · 2026-04-13 11:18:56

42

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$\sigma$-finiteness of the set of points that make measurable function equal to \infty

Published on 13 Apr 2026 - 11:18

score 319 · Answer 5 · 2026-04-15 21:01:43

319

Views

Evaluating Lebesgue integral on the unit ball

Published on 15 Apr 2026 - 21:01

score 30 · Answer 6 · 2026-04-16 18:25:46

30

Views

If $\int_{S_2}udS=0$ can we say that $u=0$ on $S_2$?

Published on 16 Apr 2026 - 18:25

score 602 · Answer 7 · 2026-04-16 07:38:17

602

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Prove that $ \lim_{n \to \infty} \int_{-\infty}^{\infty} \sin(nt) f(t) d t = 0 $.

Published on 16 Apr 2026 - 7:38

score 147 · Answer 8 · 2026-04-10 16:30:59

147

Views

Finite Sets in the sense of Lebesgue Measure

Published on 10 Apr 2026 - 16:30

score 2.8k · Answer 9 · 2026-04-15 14:49:11

2.8k

Views

if $\int fg=0$ for all continuous function $g$ then $f=0$ a.e

Published on 15 Apr 2026 - 14:49

score 310 · Answer 10 · 2026-04-13 08:19:45

310

Views

Weakest condition for a subset of $\mathbb{R}$ to have positive Lebesgue measure

Published on 13 Apr 2026 - 8:19

score 1.9k · Answer 11 · 2026-04-16 13:58:16

1.9k

Views

If a function f is differentiable then its derivate is Borel measurable

Published on 16 Apr 2026 - 13:58

score 113 · Answer 12 · 2026-04-16 05:01:44

113

Views

$\lim_{n \to \infty} f(x-n)=\lim_{n \to \infty} f(x+n)=0$ for Lebesgue integrable $f$

Published on 16 Apr 2026 - 5:01

score 1k · Answer 13 · 2026-04-12 22:20:45

1k

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Product of a sequence of functions that converges in measure and a measurable function converges in measure.

Published on 12 Apr 2026 - 22:20

score 157 · Answer 14 · 2026-04-09 19:04:25

157

Views

Relationship between the Lebesgue measure of the largest open and closed set contained in a subset of R

Published on 09 Apr 2026 - 19:04

score 60 · Answer 15 · 2026-04-14 06:46:45

60

Views

Question about a particular example of $X_n \to_p X$ but $X_n \nrightarrow_{as} X$

Published on 14 Apr 2026 - 6:46

List Question

Showing that if A$\subset$E$\subset$B and lebesgue measures of A and B are equal and finite, then E is lebesgue measurable.

A lebesgue measurable set $E$ with $\mu(E)=1$ and $\mu_F(E) = 0$.

Definition of the Lebesgue integral

$\sigma$-finiteness of the set of points that make measurable function equal to \infty

Evaluating Lebesgue integral on the unit ball

If $\int_{S_2}udS=0$ can we say that $u=0$ on $S_2$?

Prove that $ \lim_{n \to \infty} \int_{-\infty}^{\infty} \sin(nt) f(t) d t = 0 $.

Finite Sets in the sense of Lebesgue Measure

if $\int fg=0$ for all continuous function $g$ then $f=0$ a.e

Weakest condition for a subset of $\mathbb{R}$ to have positive Lebesgue measure

If a function f is differentiable then its derivate is Borel measurable

$\lim_{n \to \infty} f(x-n)=\lim_{n \to \infty} f(x+n)=0$ for Lebesgue integrable $f$

Product of a sequence of functions that converges in measure and a measurable function converges in measure.

Relationship between the Lebesgue measure of the largest open and closed set contained in a subset of R

Question about a particular example of $X_n \to_p X$ but $X_n \nrightarrow_{as} X$

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