A Fubini theorem on a function space and its applications (Q1943506)

In the analysis, Fubini's theorem gives conditions enabling to compute a double integral via iterated single integrals. There are many known versions and generalizations of this theorem in the literature. To mention just a few of them, one is known as Tonelli's theorem, another as the Kuratowski-Ulam theorem, and a third version is due to Bourbaki. Also, Cameron and Storvick established an important result which allows evaluating Feynman integrals for unbounded functionals on a Wiener space used in the context of Brownian motion. The aim of the present paper is to establish still another version for functionals on a certain function space. The usefulness of the new type of Fubini's theorem is illustrated by an example in the context of the well-known Wiener integration formula.