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On the Decomposition of A Class of Functions of Bounded Variation

Published online by Cambridge University Press:  20 November 2018

R. G. Laha
R. G. Laha*
Affiliation:
Catholic University, Washington, D.C.
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Let F1(x) and F2(x) be two distribution functions, that is, non-decreasing, right-continuous functions such that Fj(— ∞) = 0 and Fj(+ ∞) = 1 (j = 1, 2). We denote their convolution by F(x) so that

the above integrals being defined as the Lebesgue-Stieltjes integrals. Then it is easy to verify (2, p. 189) that F(x) is a distribution function. Let f1(t), f2(t), and f(t) be the corresponding characteristic functions, that is,

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 479 - 484
Copyright
Copyright © Canadian Mathematical Society 1964

References

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