Quantum measure and integration theory
Journal Article
·
· Journal of Mathematical Physics
- Department of Mathematics, University of Denver, Denver, Colorado 80208 (United States)
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.
- OSTI ID:
- 21294525
- Journal Information:
- Journal of Mathematical Physics, Vol. 50, Issue 12; Other Information: DOI: 10.1063/1.3267867; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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