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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Bibliographic Details
Published in:arXiv.org 2023-05
Main Author: Viggiano, Gianluca
Format: Article
Language:English
Subjects:
Independent variables
Taylor series
Theorem proving
Theorems
Online Access:Get full text
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Summary: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.
ISSN:2331-8422