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Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 93-96).

This paper discusses the concept of a general definition of measure, and shows that the Lebesgue measure satisfies the requirements set forth for the ideal definition.

It is the purpose of this thesis to examine and compare three Restoration and eighteenth century adaptations of Shakespeare's Measure for Measure: William Davenant's The Law Against Lovers, acted in 1662; Charles Gildon's Measure for Measure: or, Beauty the Best Advocate, acted in 1700; and John Philip Kemble's Shakspeare's Measure for Measure, acted in 1794. The plays are discussed with regard to their divergence from Shakespeare's play. In addition, they are examined from the standpoint of their ability to reflect the theatrical practices, audience preferences, and social conditions of the time in which they were performed.

In this expository paper we study the stationary measures of a stochastic process called nearest neighbor random walk on Z, and further we describe conditions for these measures to have the stronger property of reversibility. We consider both the cases of symmetric and non-symmetric random walk.

A disintegration of measure is a common tool used in ergodic theory, probability, and descriptive set theory. The primary interest in this paper is in disintegrating σ-finite measures on standard Borel spaces into families of σ-finite measures. In 1984, Dorothy Maharam asked whether every such disintegration is uniformly σ-finite meaning that there exists a countable collection of Borel sets which simultaneously witnesses that every measure in the disintegration is σ-finite. Assuming Gödel’s axiom of constructability I provide answer Maharam's question by constructing a specific disintegration which is not uniformly σ-finite.

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This thesis provides a development of integration from two different points of view. In Chapter I, a measure and a measurable function are defined. A theory of integration is then developed in Chapter II based on the measure. In Chapter III, the integral is introduced directly without first going through the process of defining a measure, and a measure is developed from the integral. The concluding chapter shows the equivalence of the two integrals under rather general conditions.

The purpose of this thesis is to study the concept of measure and associated concepts. The study is general in nature; that is, no particular examples of a measure are given.

This thesis examines measure functions. A measure function has as its domain of definition a class of sets. It also must satisfy a certain additive condition. To state a concise definition of a measure function, it is convenient to define set function and completely additive set function.