Question

Showing if $f_n\to f$ then $\mu\lbrace x: f > \alpha \rbrace \le \liminf \mu \lbrace x: f_n \ge \alpha\rbrace$

score 113 · Answer 1 · 2026-04-17 01:34:05

113

Views

Showing if $f_n\to f$ then $\mu\lbrace x: f > \alpha \rbrace \le \liminf \mu \lbrace x: f_n \ge \alpha\rbrace$

Published on 17 Apr 2026 - 1:34

score 33 · Answer 2 · 2026-04-12 15:13:34

33

Views

Relation between Lebesgue measure and nowhere denseness

Published on 12 Apr 2026 - 15:13

score 59 · Answer 3 · 2026-04-17 08:31:10

How and why do we prove that $\mathcal{l}(I) \leq \sum_{i=1}^\infty \mathcal{l}(J_i)$ where $I=\bigcup_{i=1}^\infty J_i$ is an open interval?

score 36 · Answer 4 · 2026-04-15 09:33:45

36

Views

if the function series is uniformly convergent is it also almost everywhere convergent?

Published on 15 Apr 2026 - 9:33

score 2.5k · Answer 5 · 2026-04-15 09:33:37

2.5k

Views

Is $\sin(1/x)$ Lebesgue integrable on $(0,1]$?

Published on 15 Apr 2026 - 9:33

score 1k · Answer 6 · 2026-04-13 02:15:17

1k

Views

In $\mathbb{R}^n$, $\forall B$, Borel set, there exists an disjoint countable open balls covering $B$?

Published on 13 Apr 2026 - 2:15

score 863 · Answer 7 · 2026-04-14 00:43:47

863

Views

Lebesgue measure of non-measurable set times the null set.

Published on 14 Apr 2026 - 0:43

score 68 · Answer 8 · 2026-04-17 12:22:30

68

Views

$f(x) = f_0(||x||)$, show that $f$ is measurable iff $f_0$ is measurable

Published on 17 Apr 2026 - 12:22

score 111 · Answer 9 · 2026-04-16 15:40:05

111

Views

Showing $\chi_G\notin\mathcal{R}[0,1]$ where: $G$ open, $\mathbb{Q}\cap[0,1] \subset G,$ and $m(G)<\frac{1}{2}$

Published on 16 Apr 2026 - 15:40

score 67 · Answer 10 · 2026-04-11 01:13:14

67

Views

Question about the intervals in the lebesgue measure.

Published on 11 Apr 2026 - 1:13

score 306 · Answer 11 · 2026-04-12 07:27:27

306

Views

Must any set of positive Lebesgue measure contain a bounded set of positive measure?

Published on 12 Apr 2026 - 7:27

score 38 · Answer 12 · 2026-04-15 11:19:19

38

Views

$C \subset \mathbb{R}$ finite, $\lambda(A)>0$. Prove the existence of $a$ and $b \ne 0$ such that $\{a+bx : x \in C\} \subset A$

Published on 15 Apr 2026 - 11:19

score 125 · Answer 13 · 2026-04-11 11:54:03

125

Views

$A$ not Lebesgue-measurable in $\Bbb{R} \implies A \times \Bbb{R}$ is not Lebesgue-measurable in $\Bbb{R}^2$?

Published on 11 Apr 2026 - 11:54

score 1.2k · Answer 14 · 2026-04-16 12:20:50

1.2k

Views

Check my proof -- Intersection of an open interval and a Lebesgue measurable set

Published on 16 Apr 2026 - 12:20

score 655 · Answer 15 · 2026-04-15 12:26:20

655

Views

Understing proof for the case when riemann and lebesgue-integral are the same.

Published on 15 Apr 2026 - 12:26

List Question

Showing if $f_n\to f$ then $\mu\lbrace x: f > \alpha \rbrace \le \liminf \mu \lbrace x: f_n \ge \alpha\rbrace$

Relation between Lebesgue measure and nowhere denseness

How and why do we prove that $\mathcal{l}(I) \leq \sum_{i=1}^\infty \mathcal{l}(J_i)$ where $I=\bigcup_{i=1}^\infty J_i$ is an open interval?

if the function series is uniformly convergent is it also almost everywhere convergent?

Is $\sin(1/x)$ Lebesgue integrable on $(0,1]$?

In $\mathbb{R}^n$, $\forall B$, Borel set, there exists an disjoint countable open balls covering $B$?

Lebesgue measure of non-measurable set times the null set.

$f(x) = f_0(||x||)$, show that $f$ is measurable iff $f_0$ is measurable

Showing $\chi_G\notin\mathcal{R}[0,1]$ where: $G$ open, $\mathbb{Q}\cap[0,1] \subset G,$ and $m(G)<\frac{1}{2}$

Question about the intervals in the lebesgue measure.

Must any set of positive Lebesgue measure contain a bounded set of positive measure?

$C \subset \mathbb{R}$ finite, $\lambda(A)>0$. Prove the existence of $a$ and $b \ne 0$ such that $\{a+bx : x \in C\} \subset A$

$A$ not Lebesgue-measurable in $\Bbb{R} \implies A \times \Bbb{R}$ is not Lebesgue-measurable in $\Bbb{R}^2$?

Check my proof -- Intersection of an open interval and a Lebesgue measurable set

Understing proof for the case when riemann and lebesgue-integral are the same.

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