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Definition of Borel vector field
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My doubt is what is the definition of Borel vector field? I looked for this definition on some books of geometric measure theory and on the internet, but I didn't found. The motivation for my question is that I'm reading Sets of Finite Perimeter and Geometric Variational Problem - An Introduction to Geometric Measure Theory by Francesco Maggi and the author concludes on a corollary that the derivative $D_{mu} nu$ is a Borel vector field, where $nu$ and $mu$ are Radon measures, but I don't know what this means. I thought that possibly a Borel vector field is a vector field which is a Borel function in the sense given by the author:
If $E subset mathbb{R}^n$ is a Borel set in $mathbb{R}^n$, then $u: E longrightarrow [-infty,infty]$ is a $textbf{Borel function}$ provided each ${ x in E ; u(x) > t }$ $(t in mathbb{R})$ is a Borel set.
Is this what a Borel vector field means?
Thanks in advance!
measure-theory definition geometric-measure-theory
asked Feb 1 at 17:27
GeorgeGeorge
872615
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add a comment |
$begingroup$
My doubt is what is the definition of Borel vector field? I looked for this definition on some books of geometric measure theory and on the internet, but I didn't found. The motivation for my question is that I'm reading Sets of Finite Perimeter and Geometric Variational Problem - An Introduction to Geometric Measure Theory by Francesco Maggi and the author concludes on a corollary that the derivative $D_{mu} nu$ is a Borel vector field, where $nu$ and $mu$ are Radon measures, but I don't know what this means. I thought that possibly a Borel vector field is a vector field which is a Borel function in the sense given by the author:
If $E subset mathbb{R}^n$ is a Borel set in $mathbb{R}^n$, then $u: E longrightarrow [-infty,infty]$ is a $textbf{Borel function}$ provided each ${ x in E ; u(x) > t }$ $(t in mathbb{R})$ is a Borel set.
Is this what a Borel vector field means?
Thanks in advance!
measure-theory definition geometric-measure-theory
asked Feb 1 at 17:27
GeorgeGeorge
872615
$endgroup$
add a comment |
$begingroup$
My doubt is what is the definition of Borel vector field? I looked for this definition on some books of geometric measure theory and on the internet, but I didn't found. The motivation for my question is that I'm reading Sets of Finite Perimeter and Geometric Variational Problem - An Introduction to Geometric Measure Theory by Francesco Maggi and the author concludes on a corollary that the derivative $D_{mu} nu$ is a Borel vector field, where $nu$ and $mu$ are Radon measures, but I don't know what this means. I thought that possibly a Borel vector field is a vector field which is a Borel function in the sense given by the author:
If $E subset mathbb{R}^n$ is a Borel set in $mathbb{R}^n$, then $u: E longrightarrow [-infty,infty]$ is a $textbf{Borel function}$ provided each ${ x in E ; u(x) > t }$ $(t in mathbb{R})$ is a Borel set.
Is this what a Borel vector field means?
Thanks in advance!
measure-theory definition geometric-measure-theory
asked Feb 1 at 17:27
GeorgeGeorge
872615
$endgroup$
My doubt is what is the definition of Borel vector field? I looked for this definition on some books of geometric measure theory and on the internet, but I didn't found. The motivation for my question is that I'm reading Sets of Finite Perimeter and Geometric Variational Problem - An Introduction to Geometric Measure Theory by Francesco Maggi and the author concludes on a corollary that the derivative $D_{mu} nu$ is a Borel vector field, where $nu$ and $mu$ are Radon measures, but I don't know what this means. I thought that possibly a Borel vector field is a vector field which is a Borel function in the sense given by the author:
If $E subset mathbb{R}^n$ is a Borel set in $mathbb{R}^n$, then $u: E longrightarrow [-infty,infty]$ is a $textbf{Borel function}$ provided each ${ x in E ; u(x) > t }$ $(t in mathbb{R})$ is a Borel set.
Is this what a Borel vector field means?
Thanks in advance!
measure-theory definition geometric-measure-theory
measure-theory definition geometric-measure-theory
asked Feb 1 at 17:27
GeorgeGeorge
872615
asked Feb 1 at 17:27
GeorgeGeorge
872615
asked Feb 1 at 17:27
GeorgeGeorge
872615
asked Feb 1 at 17:27
GeorgeGeorge
872615
asked Feb 1 at 17:27
GeorgeGeorge
872615
872615
add a comment |
add a comment |
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