NDLI: Integration of Functions With Values in Locally Convex Suslin Spaces

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Integration of Functions With Values in Locally Convex Suslin Spaces

Content Provider	Scilit
Author	Thomas, G. Erik F.
Copyright Year	1975
Description	The main purpose of the paper is to give some easily applicable criteria for summability of vector valued functions with respect to scalar measures. One of these is the following: If E is a quasi-complete locally convex Suslin space (e.g. a separable Banach or Fréchet space), is any total subset, and f is an E-valued function which is Pettis summable relative to the ultra weak topology . f is actually Pettis summable for the given topology. (Thus any E-valued function for which the integrals over measurable subsets can be reasonably defined as elements of E is Pettis summable.) A class of ``totally summable'' functions, generalising the Bochner integrable functions, is introduced. For these Fubini's theorem, in the case of a product measure, and the differentiation theorem, in the case of Lebesgue measure, are valid. It is shown that weakly summable functions with values in the spaces , and other conuclear spaces, are ipso facto totally summable.
Related Links	http://www.ams.org/tran/1975-212-00/S0002-9947-1975-0385067-1/S0002-9947-1975-0385067-1.pdf
Ending Page	81
Page Count	21
Starting Page	61
ISSN	00029947
e-ISSN	10886850
DOI	10.2307/1998613
Journal	Transactions of the American Mathematical Society
Volume Number	212
Language	English
Publisher	Duke University Press
Access Restriction	Open
Subject Keyword	Mathematical Physics Integration Suslin Spaces Convex Suslin Locally Convex Values Functions
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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