Question

Exercise 29 on p.40 in Exercises 2B in "Measure, Integration & Real Analysis" by Sheldon Axler.

score 85 · Answer 1 · 2023-04-05 12:44:58

85

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Exercise 29 on p.40 in Exercises 2B in "Measure, Integration & Real Analysis" by Sheldon Axler.

Published on 05 Apr 2023 - 12:44

score 73 · Answer 2 · 2023-04-11 09:58:17

73

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An expectation of a random function by varying one variable taking the others as constants

Published on 11 Apr 2023 - 9:58

score 110 · Answer 3 · 2023-04-12 09:34:06

110

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Sigma-algebra generated by conditional expectation

Published on 12 Apr 2023 - 9:34

score 51 · Answer 4 · 2026-02-25 00:46:34

51

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Counter exemple of a statement for a measurable sequence

Published on 25 Feb 2026 - 0:46

score 109 · Answer 5 · 2026-03-25 23:10:08

109

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Show that $\forall\varepsilon>0$, there exists a bounded continuous function $g(x)$ on $E$, such that $m(\{x\in E\mid f(x)\neq g(x)\})<\varepsilon$.

Published on 25 Mar 2026 - 23:10

score 41 · Answer 6 · 2023-04-18 08:38:11

41

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Restricting σ-algebra

Published on 18 Apr 2023 - 8:38

score 216 · Answer 7 · 2023-04-19 00:02:33

216

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Why is this theorem Cavalieri's Principle?

Published on 19 Apr 2023 - 0:02

score 45 · Answer 8 · 2023-04-23 12:15:42

$\sigma(\boldsymbol{\mathfrak C}) / \boldsymbol{\mathfrak B}_\mathbb R$ measurable function on $ \boldsymbol{\mathfrak C}=\{[n,n+1):n\in\mathbb Z\}.$

score 79 · Answer 9 · 2023-04-28 07:50:28

79

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(Proof Verification) Show that $\limsup_n X_n$ is tail-$\sigma$-algebra measurable for independent sequence of r.v. $(X_n)_{n=1}^\infty$.

Published on 28 Apr 2023 - 7:50

score 188 · Answer 10 · 2026-03-25 11:16:44

188

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Lebesgue measurable function and set, $\forall t\in (0,1), $there exists $ E_t \subset E$ such that $\int_{E_t} f(x) dx = t \int_{E} f(x) dx$.

Published on 25 Mar 2026 - 11:16

score 74 · Answer 11 · 2026-02-23 00:51:18

74

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Proof of the measurability of functions in Theorem 1.10 (Product measure) in "Analysis" by Lieb and Loss

Published on 23 Feb 2026 - 0:51

score 85 · Answer 12 · 2023-05-03 16:03:52

85

Views

Independent increments implies Markov property?

Published on 03 May 2023 - 16:03

score 67 · Answer 13 · 2023-05-04 20:07:33

67

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$f_{n}$ converges in measure to $f$. Prove $f_n$ converges to $f$ almost everywhere.

Published on 04 May 2023 - 20:07

score 62 · Answer 14 · 2023-05-07 21:37:45

62

Views

Upper bound for the approximation of Lebesgue integral

Published on 07 May 2023 - 21:37

score 98 · Answer 15 · 2023-05-09 11:47:04

98

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Sufficient condition that the Infimum of an uncountable family of measurable functions is measurable

Published on 09 May 2023 - 11:47

List Question

Exercise 29 on p.40 in Exercises 2B in "Measure, Integration & Real Analysis" by Sheldon Axler.

An expectation of a random function by varying one variable taking the others as constants

Sigma-algebra generated by conditional expectation

Counter exemple of a statement for a measurable sequence

Show that $\forall\varepsilon>0$, there exists a bounded continuous function $g(x)$ on $E$, such that $m(\{x\in E\mid f(x)\neq g(x)\})<\varepsilon$.

Restricting σ-algebra

Why is this theorem Cavalieri's Principle?

$\sigma(\boldsymbol{\mathfrak C}) / \boldsymbol{\mathfrak B}_\mathbb R$ measurable function on $ \boldsymbol{\mathfrak C}=\{[n,n+1):n\in\mathbb Z\}.$

(Proof Verification) Show that $\limsup_n X_n$ is tail-$\sigma$-algebra measurable for independent sequence of r.v. $(X_n)_{n=1}^\infty$.

Lebesgue measurable function and set, $\forall t\in (0,1), $there exists $ E_t \subset E$ such that $\int_{E_t} f(x) dx = t \int_{E} f(x) dx$.

Proof of the measurability of functions in Theorem 1.10 (Product measure) in "Analysis" by Lieb and Loss

Independent increments implies Markov property?

$f_{n}$ converges in measure to $f$. Prove $f_n$ converges to $f$ almost everywhere.

Upper bound for the approximation of Lebesgue integral

Sufficient condition that the Infimum of an uncountable family of measurable functions is measurable

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