Vector-valued measure as a basis of the Banach space

K. Zheltukhin, V. M. Kadets

Kharkiv State University

Abstract: A new notion of the basic measure is introdused. The vector-valued measures which are basic measures are described. It is proved that the Banach space has a basic measure iff it is isomorphic to the order continuous Banach lattice with a weak unit. The connection between the properties of the Banach space and those of the basic measure is investigated.

Received: 22.11.1997

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