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Interval Functions and Non-Decreasing Functions

Published online by Cambridge University Press:  20 November 2018

William D. L. Appling
William D. L. Appling*
Affiliation:
Duke University, Durham, North Carolina
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In a previous paper the author (1) has shown the following theorem.

Theorem A. If each of H and K is a real-valued bounded function of subintervals of the number interval [a, b] and m is a real-valued non-decreasing function on [a} b] such that each of the integrals

exists, then the integral

exists.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 752 - 754
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. L. Appling, W. D., Interval functions and the Hellinger integral, Duke Math. J., 29 (1962), 515–520.Google Scholar
2. L. Appling, W. D., Infinite series and nonnegative valued interval functions, Duke Math. J., 30 (1963), 107–112.Google Scholar
3. Hellinger, E., Die Orthogonalinvarianten quadratischer Formen von unendlichvielen Variablen, Diss., Gôttingen (1907).Google Scholar
4. Kolmogoroff, A., Untersuchung iiber den Integralbegriff, Math. Ann., 103 (1930), 654–696.Google Scholar