${\mu}$- Integrable Functions and Weak Convergence of Finite Measures

TL;DR

This paper investigates conditions for weak convergence of finite measures in metric spaces, focusing on functions valued in complete paranormed and Banach spaces, providing necessary and sufficient criteria.

Contribution

It introduces new necessary and sufficient conditions for weak convergence of finite measures involving functions in advanced vector spaces.

Findings

Established criteria for weak convergence in metric spaces

Extended results to functions in Banach and paranormed vector spaces

Provided theoretical foundations for measure convergence analysis

Abstract

This paper deals with functions that defined in metric spaces and valued in complete paranormed vector spaces or valued in Banach spaces, and obtains some necessary and sufficient conditions for weak convergence of finite measures.