Examples of measurable spaces and measurable functions other than $(mathbb{R}^n, mathcal{L}) to...
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I'm studying Lebesgue integration theory. In this theory, we study morphisms from $(mathbb{R}^n, mathcal{L})$ to $(mathbb{R}_{+}, mathcal{B})$.
Are there other interesting or important examples of morphism in the category of measurable spaces and measurable functions?
measure-theory
asked yesterday
marimo
1596
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up vote
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I'm studying Lebesgue integration theory. In this theory, we study morphisms from $(mathbb{R}^n, mathcal{L})$ to $(mathbb{R}_{+}, mathcal{B})$.
Are there other interesting or important examples of morphism in the category of measurable spaces and measurable functions?
measure-theory
asked yesterday
marimo
1596
Sure, a lot come from probability, for example, stochastic processes $mathbb{R}^mathbb{R}$ with various $sigma$-algebras.
– user10354138
yesterday
There is also a generalization of the integral for banach space valued functions. That is the Bochner integral.
– p4sch
yesterday
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I'm studying Lebesgue integration theory. In this theory, we study morphisms from $(mathbb{R}^n, mathcal{L})$ to $(mathbb{R}_{+}, mathcal{B})$.
Are there other interesting or important examples of morphism in the category of measurable spaces and measurable functions?
measure-theory
asked yesterday
marimo
1596
I'm studying Lebesgue integration theory. In this theory, we study morphisms from $(mathbb{R}^n, mathcal{L})$ to $(mathbb{R}_{+}, mathcal{B})$.
Are there other interesting or important examples of morphism in the category of measurable spaces and measurable functions?
measure-theory
measure-theory
asked yesterday
marimo
1596
asked yesterday
marimo
1596
asked yesterday
marimo
1596
asked yesterday
marimo
1596
asked yesterday
marimo
1596
1596
Sure, a lot come from probability, for example, stochastic processes $mathbb{R}^mathbb{R}$ with various $sigma$-algebras.
– user10354138
yesterday
There is also a generalization of the integral for banach space valued functions. That is the Bochner integral.
– p4sch
yesterday
add a comment |
Sure, a lot come from probability, for example, stochastic processes $mathbb{R}^mathbb{R}$ with various $sigma$-algebras.
– user10354138
yesterday
There is also a generalization of the integral for banach space valued functions. That is the Bochner integral.
– p4sch
yesterday
Sure, a lot come from probability, for example, stochastic processes $mathbb{R}^mathbb{R}$ with various $sigma$-algebras.
– user10354138
yesterday
Sure, a lot come from probability, for example, stochastic processes $mathbb{R}^mathbb{R}$ with various $sigma$-algebras.
– user10354138
yesterday
There is also a generalization of the integral for banach space valued functions. That is the Bochner integral.
– p4sch
yesterday
There is also a generalization of the integral for banach space valued functions. That is the Bochner integral.
– p4sch
yesterday
add a comment |
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Sure, a lot come from probability, for example, stochastic processes $mathbb{R}^mathbb{R}$ with various $sigma$-algebras.
– user10354138
yesterday
There is also a generalization of the integral for banach space valued functions. That is the Bochner integral.
– p4sch
yesterday