Variable Exponent Function Spaces related to a Sublinear Expectation

Abstract

In this paper, variable exponent function spaces ${\mathbb{L}}^{p\left(·\right)}$, ${\mathbb{L}}_b^{p\left(·\right)}$, and ${\mathbb{L}}_c^{p\left(·\right)}$ are introduced in the framework of sublinear expectation, and some basic and important properties of these spaces are given. A version of Kolmogorov’s criterion on variable exponent function spaces is proved for continuous modification of stochastic processes.