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Measurability of functions of two variables

Published online by Cambridge University Press:  09 April 2009

J. H. Michael  and
B. C. Rennie
J. H. Michael
Affiliation:
University of Adelaide
B. C. Rennie
Affiliation:
University of Adelaide
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Summary

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This paper investigates the existence and equality of the double and repeated integrals of a real function on a plane set. The main result (Theorem 2) is that if a function on a plane Lebesgue measurable set is continuous in one variable and measurable in the other then it is measurable in the plane.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 1 , Issue 1 , August 1959 , pp. 21 - 26
Copyright
Copyright © Australian Mathematical Society 1959

References

[1]Lichtenstein, L., Prace matematyczno-fizyczne, T. XXI, 11.Google Scholar
[2]Sierpinski, W., ‘Sur un probleme concernant les ensembles mesurables superficiellement’, Fund. Math., I (1920), 112–115.Google Scholar
[3]Sierpinski, W., ‘Sur les rapports entre l'existence des integrales: Fund. Math. I (1920), 142–147.Google Scholar