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Vector and Operator Valued Measures and Applications.
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Interval Functions and Non-Decreasing Functions
Published online by Cambridge University Press: 20 November 2018
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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.
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- Research Article
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- 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
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