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
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/34697 |
| Date | January 1970 |
| Creators | Aulakh , Pritam Singh |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For 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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