The purpose of this note is to consider the following problem. Suppose [a,b] is an interval, f a function in [a,b] and g a function which has a derivative in [a,b].
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Dyer, J. A.
"A Property of the Mean Stieltjes Integral,"
Journal of the Graduate Research Center: Vol. 33:
1, Article 4.
Available at: https://scholar.smu.edu/journal_grc/vol33/iss1/4