The Taylor Measure and its Applications

TL;DR

This paper introduces Taylor measures, a new class of signed measures, both deterministic and stochastic, that unify various concepts in mathematics and probability theory through illustrative examples.

Contribution

The paper presents a novel collection of measures called Taylor measures, including stochastic variants, unifying multiple mathematical and probabilistic concepts.

Findings

Taylor measures encompass many existing concepts as special cases.

Stochastic Taylor measures are defined and analyzed.

Examples demonstrate the unifying framework of these measures.

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.