List questions from product-measure

Published on 17 Oct 2017 - 14:31

45

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Product measure spaces: Why is it that $A_{\omega_1} = \bigcup_{n=1}^\infty (A_n)_{\omega_1}$?

Published on 23 Oct 2017 - 21:09

52

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Question regarding notation in integrals (measure theory)

Published on 29 Oct 2017 - 15:19

73

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Convergence of probability measures converging on generating set

Published on 03 Nov 2017 - 15:19

746

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Show a function defined by an integral is Borel measurable.

Published on 13 Dec 2017 - 17:28

58

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Getting Borel-measurability from a product measure space

Published on 31 Oct 2020 - 23:04

92

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$K=\{E|f^{-1}(E)\in \mathcal{S} \}$ is a $\sigma$ algebra

Published on 04 Nov 2020 - 1:01

343

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$f: X \rightarrow \mathbb{R}$ is measurable iff $\{(x, t): t=f(x)\} \in \mathcal{F} \otimes \mathcal{B}(\mathbb{R})$.

Published on 11 Nov 2020 - 1:35

364

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Show there exists a set $E \subset \mathbb{R}^2$ such that the cross sections are open subsets but $E \notin \mathcal{B}_2$.

Published on 17 Nov 2020 - 4:06

56

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How do you show that the function $f(x)=\nu(P_x)$ is measurable?

Published on 30 Dec 2020 - 22:22

167

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Show that $f$ is measurable with respect to the product measure $c \times c$.

Published on 25 Jan 2021 - 3:43

167

Views

Atomless?: product measure of an atomless measure and a measure which has atoms

Published on 27 Jan 2021 - 4:25

138

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Locally finite Borel measure on $\mathbb{R}^2$ that is not a product measure.

Published on 01 Feb 2021 - 22:24

163

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Show the left shift $T$ and $T^{-1} $ are measurable.

Published on 01 Mar 2021 - 19:08

142

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Fibered product of probability spaces

Published on 08 Jun 2021 - 0:18

List Question

Is $1_{[0,X(\omega)]}(y)$ measurable?

Product measure spaces: Why is it that $A_{\omega_1} = \bigcup_{n=1}^\infty (A_n)_{\omega_1}$?

Question regarding notation in integrals (measure theory)

Convergence of probability measures converging on generating set

Show a function defined by an integral is Borel measurable.

Getting Borel-measurability from a product measure space

$K=\{E|f^{-1}(E)\in \mathcal{S} \}$ is a $\sigma$ algebra

$f: X \rightarrow \mathbb{R}$ is measurable iff $\{(x, t): t=f(x)\} \in \mathcal{F} \otimes \mathcal{B}(\mathbb{R})$.

Show there exists a set $E \subset \mathbb{R}^2$ such that the cross sections are open subsets but $E \notin \mathcal{B}_2$.

How do you show that the function $f(x)=\nu(P_x)$ is measurable?

Show that $f$ is measurable with respect to the product measure $c \times c$.

Atomless?: product measure of an atomless measure and a measure which has atoms

Locally finite Borel measure on $\mathbb{R}^2$ that is not a product measure.

Show the left shift $T$ and $T^{-1} $ are measurable.

Fibered product of probability spaces

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