Integration on Infinite-Dimensional Spaces

Tepper L. Gill and Woodford Zachary
Additional contact information
Tepper L. Gill: Howard University, Departments of Electrical and Computer Engineering
Woodford Zachary: Howard University, Departments of Electrical and Computer Engineering

Chapter Chapter 2 in Functional Analysis and the Feynman Operator Calculus, 2016, pp 49-107 from Springer

Abstract: Abstract This chapter is required for the foundations of infinite-dimensional analysis. It is assumed that the reader is conversant with Lebesgue measure on ℝ n $$\mathbb{R}^{n}$$ , including the standard limit theorems, inequalities, convolution, Fourier transform theory, and Fubini’s theorem. With this in mind, we offer a parallel treatment on infinite-dimensional spaces, with a theorem proof protocol. The proof of any theorem that is the same as on ℝ n $$\mathbb{R}^{n}$$ is omitted. We have also added a few interesting topics, which are discussed more fully below. We do not include any exercises, however, any serious question could lead to a research problem. (This statement applies to all chapters except Chaps. 1 and 4.)

Keywords: Standard Limit Theorems; Uniformly Convex Banach Space; Countably Additive Probability Measure; Locally Compact Abelian (LCA); Admissible Translations (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-27595-6_2

Ordering information: This item can be ordered from
http://www.springer.com/9783319275956

DOI: 10.1007/978-3-319-27595-6_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().