The Henstock integral for functions with values in nuclear spaces
The Henstock integral for functions with values in nuclear spaces
The class of (UCs-N) spaces has been introduced by the author [Math. Jap. 28, 353-370 (1983; Zbl 0523.46007)] as a class of ranked vector spaces. The purpose of the present paper is to define a Henstock integral for functions with values in an (UCs-N) space and to show that the basic properties of the Henstock integral in the real-valued case also hold in this case provided that the (UCs-N) space is Hilbertian and is endowed with nuclearity. It is shown that the spaces \(S\), \(S'\), \(D\), \(D'\) of \textit{L. Schwartz} [Théorie des distributions (1966; Zbl 0149.095)] belong to the class in question.
Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.), Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), Henstock integral, nuclear space, Schwartz space, ranked vector spaces, Set functions, measures and integrals with values in ordered spaces, (UCs-N) spaces
Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.), Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), Henstock integral, nuclear space, Schwartz space, ranked vector spaces, Set functions, measures and integrals with values in ordered spaces, (UCs-N) spaces