Tepper L Gill and Woodford W Zachary
A New Class of Banach Spaces
(33K, amsart)

ABSTRACT.  In this paper, we construct a new class of separable Banach spaces ${\mathbb{KS}}^p$, which parallel the standard $L^p$ spaces, but contains each of these spaces, as well as the space of finitely additive measures, as compact dense embeddings. Equally important is the fact that these spaces contain all Henstock-Kurzweil integrable functions and, in particular, the Feynman kernel and the Dirac measure, as norm bounded elements.