Measurable Taylor's Theorem: An Elementary Proof

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only tacitly assumed. In this note, we provide an elementary...

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Published in:arXiv.org 2023-05
Main Author: Viggiano, Gianluca
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Language:English
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Independent variables
Taylor series
Theorem proving
Theorems
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description The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only tacitly assumed. In this note, we provide an elementary proof of this measurable Taylor's theorem, which guarantees that the interpolating point in the Lagrange form of the remainder can be chosen to depend measurably on the independent variable.
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subjects Independent variables
Taylor series
Theorem proving
Theorems
title Measurable Taylor's Theorem: An Elementary Proof
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