Spaces of H-Integrable Functions

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Description

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.

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63 leaves

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Wittenmyer, Eugene L. May 1968.

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This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 17 times . More information about this thesis can be viewed below.

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  • Wittenmyer, Eugene L.

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Description

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.

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63 leaves

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UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

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  • May 1968

Added to The UNT Digital Library

  • Dec. 27, 2012, 10:03 p.m.

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  • Sept. 10, 2013, 12:59 p.m.

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Citations, Rights, Re-Use

Wittenmyer, Eugene L. Spaces of H-Integrable Functions, thesis, May 1968; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc130970/: accessed September 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .