Question

Is my Proof Correct: $(X, \mathcal{A}, \mu)$ $\sigma-$finite measure space then $\mu^{*}(B) < \infty$

score 85 · Answer 1 · 2026-04-13 21:34:20

85

Views

Is my Proof Correct: $(X, \mathcal{A}, \mu)$ $\sigma-$finite measure space then $\mu^{*}(B) < \infty$

Published on 13 Apr 2026 - 21:34

score 144 · Answer 2 · 2026-04-16 08:20:41

144

Views

If $A, B \in [m,n] \subseteq \mathbb{R}$ are sets of measure zero, then is $AB = \{ab | a \in A, b \in B\}$ measure zero?

Published on 16 Apr 2026 - 8:20

score 62 · Answer 3 · 2026-04-13 20:55:41

62

Views

Example of measure for some algebra over $\mathbb N$

Published on 13 Apr 2026 - 20:55

score 56 · Answer 4 · 2026-04-15 12:32:44

56

Views

Is there an outer measure on $\mathbb R$ whose only measurable sets are $\mathbb R, \emptyset$?

Published on 15 Apr 2026 - 12:32

score 40 · Answer 5 · 2026-04-12 10:40:17

40

Views

Are Cat. II sets measurable (for a given outer measure)

Published on 12 Apr 2026 - 10:40

score 74 · Answer 6 · 2026-04-30 14:29:35

74

Views

Complete Measure spaces

Published on 30 Apr 2026 - 14:29

score 99 · Answer 7 · 2026-04-16 13:25:51

99

Views

What is the most elegant known proof of $m^(A) \leq \sum_{n} m^(A_n)$ when $A = \bigcup_n A_n$?

Published on 16 Apr 2026 - 13:25

score 294 · Answer 8 · 2026-04-13 03:40:36

294

Views

Show example $E \subset \mathbb{R}^n$ where exterior measure does not equal that of the smallest open ball cover.

Published on 13 Apr 2026 - 3:40

score 547 · Answer 9 · 2026-04-15 18:16:50

547

Views

Lebesgue outer measure of image of set is less than or equal to the Lebesgue outer measure of set

Published on 15 Apr 2026 - 18:16

score 273 · Answer 10 · 2026-04-12 22:04:11

273

Views

Subset of Lebesgue measurable subset of Vitali set is NOT Lebesgue measurable

Published on 12 Apr 2026 - 22:04

score 538 · Answer 11 · 2026-04-09 17:42:04

538

Views

Can a non-measurable set be measurable? (Seriously)

Published on 09 Apr 2026 - 17:42

score 41 · Answer 12 · 2026-04-14 19:58:52

41

Views

Weaken the condition of measurability

Published on 14 Apr 2026 - 19:58

score 64 · Answer 13 · 2026-04-16 04:36:36

$ \inf_{ \text {open sets covering E} } ( \sum \text{length}(I_n) ) \leq \inf_{ \text {closed sets covering E} } ( \sum \text{length}(J_n) ) $

score 83 · Answer 14 · 2026-04-13 09:35:40

83

Views

Example of countably additive function from a Boolean algebra to [0,infinity] that is not finitely additive

Published on 13 Apr 2026 - 9:35

score 111 · Answer 15 · 2026-04-10 03:39:15

111

Views

Proof of translation and linear transformation invariance of R_k

Published on 10 Apr 2026 - 3:39

List Question

Is my Proof Correct: $(X, \mathcal{A}, \mu)$ $\sigma-$finite measure space then $\mu^{*}(B) < \infty$

If $A, B \in [m,n] \subseteq \mathbb{R}$ are sets of measure zero, then is $AB = \{ab | a \in A, b \in B\}$ measure zero?

Example of measure for some algebra over $\mathbb N$

Is there an outer measure on $\mathbb R$ whose only measurable sets are $\mathbb R, \emptyset$?

Are Cat. II sets measurable (for a given outer measure)

Complete Measure spaces

What is the most elegant known proof of $m^(A) \leq \sum_{n} m^(A_n)$ when $A = \bigcup_n A_n$?

Show example $E \subset \mathbb{R}^n$ where exterior measure does not equal that of the smallest open ball cover.

Lebesgue outer measure of image of set is less than or equal to the Lebesgue outer measure of set

Subset of Lebesgue measurable subset of Vitali set is NOT Lebesgue measurable

Can a non-measurable set be measurable? (Seriously)

Weaken the condition of measurability

$ \inf_{ \text {open sets covering E} } ( \sum \text{length}(I_n) ) \leq \inf_{ \text {closed sets covering E} } ( \sum \text{length}(J_n) ) $

Example of countably additive function from a Boolean algebra to [0,infinity] that is not finitely additive

Proof of translation and linear transformation invariance of R_k

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