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On Measures Determined by Functions with Finite Right and Left Limits Everywhere

Published online by Cambridge University Press:  20 November 2018

H.W. Ellis  and
R. L. Jeffery
H.W. Ellis
Affiliation:
Summer Research Institute of the Canadian Mathematical Congress
R. L. Jeffery
Affiliation:
Summer Research Institute of the Canadian Mathematical Congress
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In another paper [l] measures determined from base functions, that have finite right and left limits everywhere and are of generalized bounded variation in the restricted sense, are studied and used to define non absolutely convergent integrals of Denjoy type. In this paper base functions of bounded variation and the corresponding measures are studied as a background for that paper. The results supplement parts of [2].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 2 , June 1967 , pp. 207 - 225
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Ellis, H. W. and Jeffery, R. L., Derivatives and Integrals with respect to a base function of generalized bounded variation. Canadian Journal of Mathematics vol. 19 (1966), pages 225-241.Google Scholar
2. Munroe, M. E., Introduction to Measure and Integration. Addison-Wesley, Cambridge, Mass., 1953.Google Scholar
3. Natanson, I. P., Theory of Functions of a Real Variable, translated from the Russian by L. F. Boron, Frederick Ungar, New York, 1955.Google Scholar
4. Rudin, W., Principles of Mathematical Analysis, McGraw- Hill, New York, 1953.Google Scholar
5. Saks, S., Theory of the Integral, second revised edition, Warsaw, 1937.Google Scholar