skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
 [1]
  1. 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}
}