Question

The set of discontinuities of an increasing right continuous function is closed.

score 719 · Answer 1 · 2026-04-15 04:46:12

719

Views

The set of discontinuities of an increasing right continuous function is closed.

Published on 15 Apr 2026 - 4:46

score 52 · Answer 2 · 2026-04-15 04:12:43

52

Views

Ideas on calculating the volume of $K:=\{(x,y,z)\in \mathbb R^{3}: x^2+y^2+z^2\leq 1, x^2+y^2\leq a\}$

Published on 15 Apr 2026 - 4:12

score 124 · Answer 3 · 2026-04-14 09:43:29

124

Views

Reference request: Real analysis with infinity

Published on 14 Apr 2026 - 9:43

score 56 · Answer 4 · 2026-05-05 06:44:15

56

Views

Let $\mathcal{U}$ be $\sigma$ - algebra and show $\mathcal{G}$ is $sigma$-algebra.

Published on 05 May 2026 - 6:44

score 274 · Answer 5 · 2026-04-13 16:56:41

274

Views

Prove that every signed measure $\mu$ has a decomposition into difference $\mu=\mu^+ - \mu^-$ , where $\mu^+ , \mu^-$ are measures .

Published on 13 Apr 2026 - 16:56

score 80 · Answer 6 · 2026-04-16 23:52:09

80

Views

$x=0.x_1 x_2..x_n....$ for some integer $l$

Published on 16 Apr 2026 - 23:52

score 49 · Answer 7 · 2026-04-11 20:55:46

49

Views

Measure exercise problem covering R^n with closed sets

Published on 11 Apr 2026 - 20:55

score 384 · Answer 8 · 2026-04-29 01:24:35

384

Views

$L^{q,\infty}(\mu) \subset L^p(\mu)$ with $1 \leq p<q <\infty$ and $\mu$ finite measure?

Published on 29 Apr 2026 - 1:24

score 106 · Answer 9 · 2026-04-11 17:31:20

106

Views

Problem on property of sequences of functions in Lp spaces

Published on 11 Apr 2026 - 17:31

score 29 · Answer 10 · 2026-04-09 05:12:54

29

Views

Boundedness of the measure of a compact set under a continuous family of measures

Published on 09 Apr 2026 - 5:12

score 83 · Answer 11 · 2026-04-10 04:57:17

83

Views

Prove that $\mu$ is a measure under several conditions.

Published on 10 Apr 2026 - 4:57

score 73 · Answer 12 · 2026-04-26 04:07:49

73

Views

$\|h\mu\|= \int |h|d|\mu|$

Published on 26 Apr 2026 - 4:07

score 170 · Answer 13 · 2026-05-11 06:34:33

170

Views

Is every $\sigma$-algebra a Borel $\sigma$-algebra?

Published on 11 May 2026 - 6:34

score 46 · Answer 14 · 2026-04-14 19:45:50

46

Views

Determine $\varphi_{\epsilon}$

Published on 14 Apr 2026 - 19:45

score 55 · Answer 15 · 2026-04-11 19:20:23

55

Views

Express $\{f\leq c\}$ as a countable intersection

Published on 11 Apr 2026 - 19:20

List Question

The set of discontinuities of an increasing right continuous function is closed.

Ideas on calculating the volume of $K:=\{(x,y,z)\in \mathbb R^{3}: x^2+y^2+z^2\leq 1, x^2+y^2\leq a\}$

Reference request: Real analysis with infinity

Let $\mathcal{U}$ be $\sigma$ - algebra and show $\mathcal{G}$ is $sigma$-algebra.

Prove that every signed measure $\mu$ has a decomposition into difference $\mu=\mu^+ - \mu^-$ , where $\mu^+ , \mu^-$ are measures .

$x=0.x_1 x_2..x_n....$ for some integer $l$

Measure exercise problem covering R^n with closed sets

$L^{q,\infty}(\mu) \subset L^p(\mu)$ with $1 \leq p<q <\infty$ and $\mu$ finite measure?

Problem on property of sequences of functions in Lp spaces

Boundedness of the measure of a compact set under a continuous family of measures

Prove that $\mu$ is a measure under several conditions.

$\|h\mu\|= \int |h|d|\mu|$

Is every $\sigma$-algebra a Borel $\sigma$-algebra?

Determine $\varphi_{\epsilon}$

Express $\{f\leq c\}$ as a countable intersection

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