Question

Where am I wrong about Borel-Cantelli Lemma

score 49 · Answer 1 · 2021-04-15 13:03:16

49

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Where am I wrong about Borel-Cantelli Lemma

Published on 15 Apr 2021 - 13:03

score 106 · Answer 2 · 2021-04-18 10:34:39

106

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Why should an outer measure give 0 on an empty set?

Published on 18 Apr 2021 - 10:34

score 72 · Answer 3 · 2021-04-18 20:18:01

Show that a function $f : X \to [−∞, +∞]$ is measurable with respect to $μ^∗$ if and only if $μ^∗(T)≥μ^∗(T∩{x∈X:f(x)≤a})+μ^∗(T∩{x∈X:f(x)≥b})$

score 36 · Answer 4 · 2021-04-21 23:36:50

36

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About the theorem for an open subset $O$ of $R^{d}$.

Published on 21 Apr 2021 - 23:36

score 143 · Answer 5 · 2021-04-23 08:48:46

143

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About proof of "Exterior measure of a closed cube is equal to its volume".

Published on 23 Apr 2021 - 8:48

score 185 · Answer 6 · 2021-04-24 07:39:22

185

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Understanding the proof of non-additivity of outer measure

Published on 24 Apr 2021 - 7:39

score 49 · Answer 7 · 2021-04-26 17:01:13

49

Views

Proving that $(X, \mathcal A, \mu^)$ is the completion of $(X, \sigma (\mathcal A_0), \mu^).$

Published on 26 Apr 2021 - 17:01

score 76 · Answer 8 · 2021-04-27 02:45:15

76

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Can we say that $\mathcal A = \mathcal A^*\ $?

Published on 27 Apr 2021 - 2:45

score 84 · Answer 9 · 2021-04-29 08:12:55

84

Views

Show that there exist $G,H \in \sigma (\mathcal A_0)$ with $H \subseteq A \subseteq G$ such that $\mu^* (G \setminus H) = 0.$

Published on 29 Apr 2021 - 8:12

score 87 · Answer 10 · 2021-05-02 05:17:41

87

Views

characterization of positive measure

Published on 02 May 2021 - 5:17

score 38 · Answer 11 · 2021-05-03 15:02:36

38

Views

Intuition about non measurable sets in $\mathbb R^d$

Published on 03 May 2021 - 15:02

score 471 · Answer 12 · 2021-05-07 02:26:31

471

Views

Bartle exercise 9.N from elements of integration

Published on 07 May 2021 - 2:26

score 349 · Answer 13 · 2026-03-25 12:54:19

349

Views

Hahn Decomposition Theorem and Jordan Decomposition for Finite Signed Pre-measures

Published on 25 Mar 2026 - 12:54

score 117 · Answer 14 · 2021-05-19 13:10:09

117

Views

Give an example of failure of the continuity of outer Lebesgue measure

Published on 19 May 2021 - 13:10

score 71 · Answer 15 · 2021-05-20 22:54:04

71

Views

Equivalence of measurable sets

Published on 20 May 2021 - 22:54

List Question

Where am I wrong about Borel-Cantelli Lemma

Why should an outer measure give 0 on an empty set?

Show that a function $f : X \to [−∞, +∞]$ is measurable with respect to $μ^∗$ if and only if $μ^∗(T)≥μ^∗(T∩{x∈X:f(x)≤a})+μ^∗(T∩{x∈X:f(x)≥b})$

About the theorem for an open subset $O$ of $R^{d}$.

About proof of "Exterior measure of a closed cube is equal to its volume".

Understanding the proof of non-additivity of outer measure

Proving that $(X, \mathcal A, \mu^)$ is the completion of $(X, \sigma (\mathcal A_0), \mu^).$

Can we say that $\mathcal A = \mathcal A^*\ $?

Show that there exist $G,H \in \sigma (\mathcal A_0)$ with $H \subseteq A \subseteq G$ such that $\mu^* (G \setminus H) = 0.$

characterization of positive measure

Intuition about non measurable sets in $\mathbb R^d$

Bartle exercise 9.N from elements of integration

Hahn Decomposition Theorem and Jordan Decomposition for Finite Signed Pre-measures

Give an example of failure of the continuity of outer Lebesgue measure

Equivalence of measurable sets

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