The Multivariate Taylor Measure Function Space and a Generalization of Taylor's Theorem

TL;DR

This paper introduces a generalized Taylor theorem applicable to measurable, non-analytic functions without differentiation, leading to a new function space called multivariate Taylor measure function space, unifying various mathematical concepts.

Contribution

It proposes a novel generalization of Taylor's theorem for non-analytic functions and defines a new function space, broadening the scope of Taylor measure applications.

Findings

Defined multivariate Taylor measure function space

Established properties of the new function space

Unified multiple mathematical concepts under the generalization

Abstract

Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the definition and properties of a new space of functions, which will be called multivariate Taylor measure function space. The proposed generalization emerges as a unifying framework that includes many concepts from mathematics as special cases.