Inaugural dissertation--Universität Bonn.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 20-21).

Semicontinuity, a concept credited to Baire by Edgar Phillips, is an important generalization of the definition of continuity and can be obtained by dropping a portion of the requirements imposed upon a continuous function. The purpose of this paper is to present a number of theorems on semicontinuity and to use these results in the development of the Daniell integral. / Advisor: Dwight B. Goodner, Professor Directing Paper. / Typescript. / "August, 1955." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaf 29).

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The problem with which this paper is concerned is that of investigating the properties of an integral which was first defined by E. J. McShane in lecture notes presented at the Conference on Modern Theories of Integration, held at the University of Oklahoma in June, 1969.

In this thesis we consider integrals of a certain class of interval functions. Specifically we consider a nondegenerate number interval [a,b], a real valued function m, defined and nondecreasing on [a,b], and the set Hm, of real valued functions f, defined on [a,b] such that: 1) f(a)=0; 2) for each subinterval [p,q] of [a,b], if m(q)-m(p)=0, then f(q)-f(p)=0; and 3) the set of all sums of the form Σ(Δf)2/Δm for subdivisions D of [a,b] is bounded above.