Question

Outer measure on $\mathbb R$ some sort of continuity about Measure

score 55 · Answer 1 · 2026-04-17 07:36:18

55

Views

Outer measure on $\mathbb R$ some sort of continuity about Measure

Published on 17 Apr 2026 - 7:36

score 864 · Answer 2 · 2026-05-10 15:53:45

864

Views

Let $m^\ast(E)$ < ∞.If for every interval (a, b) we have that $b-a$=$m^\ast((a,b)∩E) + m^\ast((a,b) ∩ E^c)$ then $E$ is lebesgue measurable

Published on 10 May 2026 - 15:53

score 102 · Answer 3 · 2026-04-14 22:26:02

102

Views

Show that for every $A \subseteq \mathbb{R}$ there exists a measurable set $A\subseteq E \subseteq \mathbb{R}$ such that $m^*(A) = m(E)$

Published on 14 Apr 2026 - 22:26

score 80 · Answer 4 · 2026-04-16 21:00:12

80

Views

show $m^(E_1\cup E_2) = m^(E_1)+m^*(E_2)$ where the distance is positive

Published on 16 Apr 2026 - 21:00

score 171 · Answer 5 · 2026-05-10 18:04:26

171

Views

Is the $\sigma$-algebra generated by the Carathéodory condition maximal?

Published on 10 May 2026 - 18:04

score 232 · Answer 6 · 2026-04-10 18:06:26

232

Views

Why does the proof of countable subadditivity of the outermeasure require translating to intervals?

Published on 10 Apr 2026 - 18:06

score 357 · Answer 7 · 2026-04-13 10:54:46

357

Views

Continuity from below for regular outer measures.

Published on 13 Apr 2026 - 10:54

score 972 · Answer 8 · 2026-04-17 15:31:58

972

Views

Why must there be disjoint sets $A$ and $B$ such that $m^(A \cup B) < m^(A) + m^*(B)$? (Theorem 18, Royden)

Published on 17 Apr 2026 - 15:31

score 73 · Answer 9 · 2026-04-12 10:02:51

73

Views

Approximation theorem for measures - proof unclear

Published on 12 Apr 2026 - 10:02

score 204 · Answer 10 · 2026-04-14 14:19:21

204

Views

Outer Measure of the set $E=(\mathbb Q\times \mathbb R) \cup (\mathbb R\times \mathbb Q)$

Published on 14 Apr 2026 - 14:19

score 20 · Answer 11 · 2026-04-09 05:34:30

20

Views

Explanation of a step in a solution.

Published on 09 Apr 2026 - 5:34

score 313 · Answer 12 · 2026-05-10 17:36:26

313

Views

upper bound of outer measure on compact support of continuous function

Published on 10 May 2026 - 17:36

score 168 · Answer 13 · 2026-04-15 16:10:45

168

Views

Outer measure of $\mathbb{Q}\times \mathbb{R}$

Published on 15 Apr 2026 - 16:10

score 55 · Answer 14 · 2026-04-16 17:20:01

55

Views

Question regarding the Lebesgue outer measure and open intervals.

Published on 16 Apr 2026 - 17:20

score 26 · Answer 15 · 2026-04-11 15:37:32

26

Views

Showing that the limit exists within the definition of set function

Published on 11 Apr 2026 - 15:37

List Question

Outer measure on $\mathbb R$ some sort of continuity about Measure

Let $m^\ast(E)$ < ∞.If for every interval (a, b) we have that $b-a$=$m^\ast((a,b)∩E) + m^\ast((a,b) ∩ E^c)$ then $E$ is lebesgue measurable

Show that for every $A \subseteq \mathbb{R}$ there exists a measurable set $A\subseteq E \subseteq \mathbb{R}$ such that $m^*(A) = m(E)$

show $m^(E_1\cup E_2) = m^(E_1)+m^*(E_2)$ where the distance is positive

Is the $\sigma$-algebra generated by the Carathéodory condition maximal?

Why does the proof of countable subadditivity of the outermeasure require translating to intervals?

Continuity from below for regular outer measures.

Why must there be disjoint sets $A$ and $B$ such that $m^(A \cup B) < m^(A) + m^*(B)$? (Theorem 18, Royden)

Approximation theorem for measures - proof unclear

Outer Measure of the set $E=(\mathbb Q\times \mathbb R) \cup (\mathbb R\times \mathbb Q)$

Explanation of a step in a solution.

upper bound of outer measure on compact support of continuous function

Outer measure of $\mathbb{Q}\times \mathbb{R}$

Question regarding the Lebesgue outer measure and open intervals.

Showing that the limit exists within the definition of set function

Trending Questions

Popular # Hahtags

Popular Questions