Representation of the Dirac delta function in $\mathcal{C}(R^{\infty})$ in terms of infinite-dimensional Lebesgue measures

TL;DR

This paper presents a novel representation of the Dirac delta function within the space of continuous functions over infinite-dimensional Euclidean space, utilizing infinite-dimensional Lebesgue measures, and explores its properties.

Contribution

It introduces a new way to represent the Dirac delta function in infinite-dimensional spaces using Lebesgue measures, expanding the theoretical framework.

Findings

Representation of the delta function in $\mathcal{C}(\mathbb{R}^\infty)$

Properties of the delta function in infinite-dimensional Lebesgue measure context

Potential applications in infinite-dimensional analysis

Abstract

A representation of the Dirac delta function in $ \mathcal{C}(R^{\infty})$ in terms of infinite-dimensional Lebesgue measures in $R^{\infty}$ is obtained and some it's properties are studied in this paper.