The Taylor Measure and its Applications

Abstract

We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We illustrate, through examples, how the deterministic and stochastic versions of the proposed Taylor measures emerge as a unifying framework that includes many concepts from mathematics and probability theory as special cases.

22 pages, definitions of the Taylor measure, Taylor probability measures, Stochastic Taylor measure, and generalization of Taylor's Theorem