%0 Journal Article
%T Quantum measure and integration theory
%A Stan Gudder
%J Mathematics
%D 2009
%I arXiv
%R 10.1063/1.3267867
%X This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum integral's form for simple functions is characterized and it is shown that the quantum integral generalizes the Lebesgue integral. A bounded, monotone convergence theorem for quantum integrals is obtained and it is shown that a Radon-Nikodym type theorem does not hold for quantum measures. As an example, a quantum-Lebesgue integral on the real line is considered.
%U http://arxiv.org/abs/0909.2203v1