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Representation of additive and biadditive nonlinear functionals

In this thesis we are concerned with obtaining an integral representation of a class of nonlinear additive and biadditive functionals on function spaces of measurable functions and on L[superscript] p-spaces, p > 0 . The associated measure space is essentially atom-free finite and o-finite.
Also we are concerned to the extend the presence of atoms in a measure space complicates the representation theory for functionals of the type under consideration here.
A class of nonlinear transformations on L[superscript] p-spaces, 1 ≤ p ≤ ∞, called Urysohn operators. [11] taking measurable functions to measurable functions is studied and we describe an integral representation for this class when the associated measure space is an arbitrary 0-finite measure space and this characterization extends our previous results where the measure space considered was atom-free. / Science, Faculty of / Mathematics, Department of / Graduate

Identiferoai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/34697
Date January 1970
CreatorsAulakh , Pritam Singh
PublisherUniversity of British Columbia
Source SetsUniversity of British Columbia
LanguageEnglish
Detected LanguageEnglish
TypeText, Thesis/Dissertation
RightsFor non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

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