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A note on the countable chain condition and sigma-finiteness of measures

Published online by Cambridge University Press:  17 April 2009

K.P.S. Bhaskara Rao  and
M. Bhaskara Rao
K.P.S. Bhaskara Rao
Affiliation:
Research and Training School, Indian Statistical Institute, Calcutta, India.
M. Bhaskara Rao
Affiliation:
Research and Training School, Indian Statistical Institute, Calcutta, India.
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The objectives of this paper are the following:

(1) to show that a theorem of Ficker is incorrect;

(2) to show that a stronger version of Ficker's Theorem is valid for a certain class of measures;

(3) characterize all σ-algebras on which every measure is a countable sum of finite measures.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 3 , June 1972 , pp. 349 - 353
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Ficker, V., “On the equivalence of a countable disjoint class of sets of positive measure and a weaker condition than total σ-finiteness of measures”, Bull. Austral. Math. Soc. 1 (1969). 237–243.Google Scholar
[2]Halmos, Paul R., Lectures on Boolean algebras (Van Nostrand, Princeton, New Jersey; Toronto; New York; London; 1963).Google Scholar
[3]Rao, B.V., “On Borel structures”, Colloq. Math. 21 (1970), 199–204.Google Scholar