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

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.