Quantum measure and integration theory
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.
- Authors:
-
- Department of Mathematics, University of Denver, Denver, Colorado 80208 (United States)
- Publication Date:
- OSTI Identifier:
- 21294525
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Mathematical Physics
- Additional Journal Information:
- Journal Volume: 50; Journal Issue: 12; Other Information: DOI: 10.1063/1.3267867; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CONVERGENCE; INTEGRALS; MATHEMATICAL SPACE; MEASURE THEORY; QUANTUM MECHANICS
Citation Formats
Gudder, Stan. Quantum measure and integration theory. United States: N. p., 2009.
Web. doi:10.1063/1.3267867.
Gudder, Stan. Quantum measure and integration theory. United States. https://doi.org/10.1063/1.3267867
Gudder, Stan. 2009.
"Quantum measure and integration theory". United States. https://doi.org/10.1063/1.3267867.
@article{osti_21294525,
title = {Quantum measure and integration theory},
author = {Gudder, Stan},
abstractNote = {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.},
doi = {10.1063/1.3267867},
url = {https://www.osti.gov/biblio/21294525},
journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 12,
volume = 50,
place = {United States},
year = {Tue Dec 15 00:00:00 EST 2009},
month = {Tue Dec 15 00:00:00 EST 2009}
}
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