Convergence for varying measures

TL;DR

This paper establishes limit theorems for sequences of functions with varying measures, demonstrating convergence in both weak and strong senses in scalar, vector, and multivalued contexts.

Contribution

It introduces new limit theorems for integrals of functions with changing measures, extending classical results to vector and multivalued function settings.

Findings

Proves convergence theorems for scalar functions with varying measures.

Extends convergence results to vector-valued functions.

Establishes weak and strong convergence in multivalued function spaces.

Abstract

Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.