Tensor Integral: A New Comprehensive Approach to the Integration Theory
Mangatiana A. Robdera *
Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana.
*Author to whom correspondence should be addressed.
Abstract
We use tensor product to introduce a new approach to the theory of integration. Such an approach will strengthen the existing various classical concepts of integral and will provide a continuous thread tying the subject matter together. The integral of vector-valued functions with respect to vector-valued additive measures will be covered without any assumption of measurability. As applications, we state and prove extensions of the Lebesgue fundamental theorems of convergence in a more general setting.
Keywords: Vector integral, tensor product, additive measure.