The Mean Value for Infinite Volume Measures, Infinite Products, and Heuristic Infinite Dimensional Lebesgue Measures
Author
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-01-30
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
One of the goals of this article is to describe a setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure and of the concentration property on metric measured spaces, inspired from classical examples of means.
In some cases, we get a linear extension of the limit at infinity.
Then, the mean value on an infinite product is defined, first for cylindrical functions and secondly taking the uniform limit.
Finally, the mean value for the heuristic Lebesgue measure on a separable infinite dimensional topological vector space (e.g., on a Hilbert space) is defined.
This last object, which is not the classical infinite dimensional Lebesgue measure but its “normalized” version, is shown to be invariant under translation, scaling, and restriction.
American Psychological Association (APA)
Magnot, Jean-Pierre. 2017. The Mean Value for Infinite Volume Measures, Infinite Products, and Heuristic Infinite Dimensional Lebesgue Measures. Journal of Mathematics،Vol. 2017, no. 2017, pp.1-14.
https://search.emarefa.net/detail/BIM-1182408
Modern Language Association (MLA)
Magnot, Jean-Pierre. The Mean Value for Infinite Volume Measures, Infinite Products, and Heuristic Infinite Dimensional Lebesgue Measures. Journal of Mathematics No. 2017 (2017), pp.1-14.
https://search.emarefa.net/detail/BIM-1182408
American Medical Association (AMA)
Magnot, Jean-Pierre. The Mean Value for Infinite Volume Measures, Infinite Products, and Heuristic Infinite Dimensional Lebesgue Measures. Journal of Mathematics. 2017. Vol. 2017, no. 2017, pp.1-14.
https://search.emarefa.net/detail/BIM-1182408
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1182408