Year: 2009
Type: article
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.
Source: Journal of Mathematical Physics
DOI: 10.1063/1.3267867
Author: Stan Gudder
Institution: University of Denver
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2009100717