The multivariate Taylor measure function space and a generalization of Taylor’s theorem

We propose a generalization of Taylor’s theorem to measurable, non-analytic functions that do not require differentiation. We study the consequences of the generalization, including the definition and properties of a new space of functions, which will be called the multivariate Taylor measure function space. We illustrate through examples that the proposed generalization emerges as a unifying framework that includes many concepts from mathematics as special cases. Applications of the new function space are also presented regarding solutions to linear and non-linear ordinary differential equations and partial differential equations.