Quantum measure and integration theory

Details Quantum measure and integration theory Quantum measure and integration theory

2009-09-11

arxiv.org/abs/0909.2203v1

J.Math.Phys.50:123509,2009

Physics

Quantum Physics

28 pages

Scientific paper

10.1063/1.3267867

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.

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