The Integration of Stepanov Remotely Almost Periodic Functions

TL;DR

This paper investigates the integration properties of Stepanov remotely almost periodic functions, proving that their primitives with minimal omega-limit sets are also remotely almost periodic, confirming a prior conjecture.

Contribution

It establishes that primitives of Stepanov remotely almost periodic functions with minimal omega-limit sets are also remotely almost periodic, confirming a previously conjectured property.

Findings

Primitives of these functions are remotely almost periodic.

The conjecture about the property of primitives is proven.

The result applies to functions with minimal omega-limit sets.

Abstract

The aim of this paper is to study the problem of the integration of Stepanov remotely almost periodic functions. We prove that every compact primitive of a Stepanov remotely almost periodic function with a minimal $\omega$-limit set is remotely almost periodic. This fact proves the conjecture previously formulated by the author.