International Journal of Statistics and Applied Mathematics
2019, Vol. 4, Issue 5, Part A
Integral in topological spacesAuthor(s):
Farhat Jabeen and Dr. Chitra SinghAbstract:
Let X, Y be Banach spaces (or either topological vector spaces) and let us consider the function space C (S, X) of all continuous functions f: S → X, from the compact (locally compact) space S into X, equipped with some appropriate topology. Put C (S, X) = C (S) if X = R. In this work we will mainly be concerned with the problem of representing linear bounded operators T: C (S, X) → Y in an integral form: f ∈ C (S, X), Tf =R S f dµ, for some integration process with respect to a measure µ on the Borel σ−ﬁeld BS of S. The prototype of such representation is the theorem of F. Riesz according to which every continuous functional T: C (S) → R has the Lebesgue integral form Tf =R S f dµ. This paper is intended to present various extensions of this theorem to the Banach spaces setting alluded to above, and to the context of locally convex spaces.Pages: 08-10 | Views: 306 | Downloads: 22Download Full Article: Click Here
How to cite this article:
Farhat Jabeen, Dr. Chitra Singh. Integral in topological spaces. Int J Stat Appl Math 2019;4(5):08-10.