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• 1 University of Burdwan Department of Mathematics Burdwan 713 104 West Bengal India
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## Abstract

The tensor integral of a vector valued function f: Ω → X with respect to a countably additive vector valued measure v: Σ → Y has been defined by Stefansson in [14] and he has investigated many of its properties. The integral is an element of the injective tensor product X

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Y. We study the Banach space L1(v, X, Y) of all
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-integrable functions and discuss many properties of this space. We also study the space w-L1(v, X, Y) of all weakly
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-integrable functions.

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