Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures

This work addresses the problem of defining characteristic kernels for machine learning applications on complex mathematical spaces, which is incremental but extends existing theory to broader domains.

The paper introduces new classes of positive definite kernels that are integrally strictly positive definite or characteristic on non-standard spaces such as Hilbert spaces, Banach spaces, and sets of measures, providing explicit examples for separable L^p spaces and measure sets.