Tensor Integral: A new comprehensive approach to the integration theory
PublisherSCIENCEDOMAIN International, www.sciencedomain.org
RightsIt is available under Creative Common Attribution License
Rights holderRobdera, M. (2014)Tensor Integral: a new comprehensive approach to the integration theory, British Journal of Mathematics & Computer Science, Vol. 4, No. 22, pp 3236-3244
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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.