Date of Award

11-1980

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Supervisor

Professor C. Bennett

Abstract

This thesis gives a historical account of the development of the theory of spaces of measurable functions. The study will be mainly centred around Holder's inequality and its many generalizations.

We present a formal axiomatization of the theory including a general form of Holder's inequality. Then we consider various families of spaces of measurable functions, namely the Orlicz spaces and the Lorentz spaces, both of which include the familiar LP-species. In each of these special cases, Holder's inequality is interesting in its own right. As a particular example, the space Llog⁺L and its conjugate, the exponential space, are studied in detail as they are examples of both an Orlicz space and a Lorentz space.


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