On a result of D.W. Stroock

TL;DR

This paper demonstrates that any universally Gaussian measurable additive map between separable Banach spaces is necessarily continuous and linear, extending Stroock's argument to establish this fundamental property.

Contribution

It adapts Stroock's argument to prove the continuity and linearity of universally Gaussian measurable additive maps between separable Banach spaces.

Findings

Universally Gaussian measurable additive maps are continuous.

Such maps are necessarily linear.

The argument extends Stroock's original approach.

Abstract

We show how to modify an argument of D. W. Stroock to show that an additive map from one separable Banach space to another, that is "universally Gaussian measurable", must be continuous (hence linear).