Year: 2024
Type: article
Abstract: We study an integration theory on general measure spaces without imposing the convention infinity times zero equals zero. Our approach depends upon the premises concerning the countable additivity of the corresponding measure and the fact that the measure of the empty set is zero. An outstanding feature of this approach concerns the fact that all the results obtained in this paper are implied by the Third Littlewood’s principle and a Fundamental Theorem asserting that if a bounded real-valued function defined on a set of finite measure is measurable then it is integrable.
Source: Journal of Mathematical Analysis
Authors: Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Departamento de Matematicas, Ciudad de Mexico 04510, Mexico, GERARDO SANCHEZ LICEA
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4406587332