Variable exponent function spaces related to a sublinear expectation (Q2303078)

Summary: In this paper, variable exponent function spaces \(\mathbb{L}^{p \left(\cdot\right)}\), \(\mathbb{L}_b^{p \left(\cdot\right)} \), and \(\mathbb{L}_c^{p \left(\cdot\right)}\) 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.