Ergodic Theorem in Grand Variable Exponent Lebesgue Spaces

TL;DR

This paper explores fundamental properties and ergodic theorems within grand variable exponent Lebesgue spaces, focusing on cases where the exponent remains invariant under transformations.

Contribution

It introduces new results on ergodic theorems in grand variable exponent Lebesgue spaces with invariant exponents, expanding the theoretical framework.

Findings

Established properties of grand variable exponent Lebesgue spaces.

Proved ergodic theorems for invariant exponents in these spaces.

Extended classical ergodic results to a broader functional setting.

Abstract

We consider several fundamental properties of grand variable exponent Lebesgue spaces. Moreover, we discuss Ergodic theorems in these spaces whenever the exponent is invariant under the transformation.