Question

Construct an interesting subset of R which is Lebesgue measurable

score 42 · Answer 1 · 2023-03-06 04:48:14

42

Views

Construct an interesting subset of R which is Lebesgue measurable

Published on 06 Mar 2023 - 4:48

score 112 · Answer 2 · 2026-02-24 13:35:04

112

Views

Convergence of a mollifier function.

Published on 24 Feb 2026 - 13:35

score 73 · Answer 3 · 2023-03-19 13:52:31

73

Views

How can I prove this equivalent relation about measurable random variables?

Published on 19 Mar 2023 - 13:52

score 27 · Answer 4 · 2023-04-16 20:03:05

27

Views

Lebesgue measure of a set $A \in (a,b)$ can be bounded by $b+a + |t|$ where $t$ is a translation constant

Published on 16 Apr 2023 - 20:03

score 30 · Answer 5 · 2023-04-18 04:17:56

30

Views

Borel Measurability of a subset of $R^{\infty}$

Published on 18 Apr 2023 - 4:17

score 187 · Answer 6 · 2023-04-29 21:21:54

187

Views

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 29 Apr 2023 - 21:21

score 128 · Answer 7 · 2023-05-09 08:50:36

128

Views

$\frac{1}{m(E)}\int _E f(x) dx\in S$ implies $f(x)\in S$ for a.e. $x$

Published on 09 May 2023 - 8:50

score 100 · Answer 8 · 2023-05-24 13:04:02

100

Views

Elementary functions are measurable

Published on 24 May 2023 - 13:04

score 49 · Answer 9 · 2023-05-24 19:24:19

49

Views

Right-continuous, real valued functions of a real variable are $\mathcal{B}$-measurable

Published on 24 May 2023 - 19:24

score 28 · Answer 10 · 2023-06-24 11:37:10

28

Views

$f: E \rightarrow \mathbb{R}$ is $\mathcal{E}$-measurable if and only if $f^{+}$ and $f^{-}$ are $\mathcal{E}$-measurable

Published on 24 Jun 2023 - 11:37

score 65 · Answer 11 · 2023-06-25 01:05:22

65

Views

Unions of $\sigma$-algebras (joint $\sigma$-algebra equals the $\sigma$-algebra generated by all finite instersections)

Published on 25 Jun 2023 - 1:05

score 58 · Answer 12 · 2023-07-05 11:46:03

58

Views

Prove that a set is measurable.

Published on 05 Jul 2023 - 11:46

score 72 · Answer 13 · 2023-07-11 06:33:40

72

Views

Definition of measurable sets

Published on 11 Jul 2023 - 6:33

score 57 · Answer 14 · 2023-08-02 06:34:30

57

Views

Show that $E^-$ is Lebesgue measurable.

Published on 02 Aug 2023 - 6:34

score 137 · Answer 15 · 2023-08-19 08:24:28

137

Views

Show that $S$ has Lebesgue measure zero.

Published on 19 Aug 2023 - 8:24

List Question

Construct an interesting subset of R which is Lebesgue measurable

Convergence of a mollifier function.

How can I prove this equivalent relation about measurable random variables?

Lebesgue measure of a set $A \in (a,b)$ can be bounded by $b+a + |t|$ where $t$ is a translation constant

Borel Measurability of a subset of $R^{\infty}$

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

$\frac{1}{m(E)}\int _E f(x) dx\in S$ implies $f(x)\in S$ for a.e. $x$

Elementary functions are measurable

Right-continuous, real valued functions of a real variable are $\mathcal{B}$-measurable

$f: E \rightarrow \mathbb{R}$ is $\mathcal{E}$-measurable if and only if $f^{+}$ and $f^{-}$ are $\mathcal{E}$-measurable

Unions of $\sigma$-algebras (joint $\sigma$-algebra equals the $\sigma$-algebra generated by all finite instersections)

Prove that a set is measurable.

Definition of measurable sets

Show that $E^-$ is Lebesgue measurable.

Show that $S$ has Lebesgue measure zero.

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