Quantum measure and integration theory
arXiv:0909.2203 · doi:10.1063/1.3267867
Abstract
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.
28 pages
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Cited by in corpus (16)
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