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 …
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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.
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