Vol. 44, No. 1, 1973

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A mean Stieltjes type integral

Dean Blackburn Priest

Vol. 44 (1973), No. 1, 291–297
Abstract

For the extended mean Stieltjes integral R. A. Stokes has shown that joint discontinuities of the functions involved can be ignored just as in the ordinary mean Stieltjes integral as considered by Porcelli and others. A Stieltjes type integral of a function with respect to a function pair has been defind by E. D. Roach, but existence of the integral depends upon the simultaneous continuity of two or more of the functions involved. In this paper a mean Stieltjes type integral of a function with respect to a function pair is defined which overcomes these limitations. Representation theorems for the integral are also given.

Mathematical Subject Classification 2000
Primary: 26A42
Milestones
Received: 30 August 1971
Revised: 24 March 1972
Published: 1 January 1973
Authors
Dean Blackburn Priest