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The Mean Integral

The purpose of this paper is to examine properties of the mean integral. The mean integral is compared with the regular integral. If [a;b] is an interval, f is quasicontinuous on [a;b] and g has bounded variation on [a;b], then the man integral of f with respect to g exists on [a;b]. The following theorem is proved. If [a*;b*] and [a;b] each is an interval and h is a function from [a*;b*] into R, then the following two statements are equivalent: 1) If f is a function from [a;b] into [a*;b*], gi is a function from [a;b] into R with bounded variation and (m)∫^b_afdg exists then (m)∫^b_ah(f)dg exists. 2) h is continuous.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc500820
Date12 1900
CreatorsSpear, Donald W.
ContributorsAppling, William D. L., Neuberger, John W.
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatiii, 45 leaves, Text
RightsPublic, Spear, Donald W., Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved.

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