The integral representation of vector measures on a completely regular space

O. E. Tsitritskii

Kiev State University

Abstract: We consider the vector space $C(X,E)$ of all bounded continuous functions from a completely regular space $X$ into a Banach space $E$. It is given a special locally convex topology $\xi$. We prove the analog of the Riesz–Markov theorem for the $\xi$-continuous linear operators which map $C(X,E)$ into a Banach space $F$.

UDC: 519

Received: 04.07.1975

 English version: Mathematical Notes, 1976, 20:3, 780–784

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