This article is cited in 2 papers

Four counterexamples to the Fubini theorem

A. V. Uglanov

P. G. Demidov Yaroslavl State University

Abstract: In this paper we study signed measures. Our main results are as follows: the Fubini theorem is not true in the general case; the Jordan parts of a transition measure are not necessarily transition measures; the operation of taking the Jordan parts does not necessarily commute with multiplying by the initial measure; the product of $\sigma$-bounded measures need not be a $\sigma$-bounded measure.

UDC: 517

Received: 11.04.1994

DOI: 10.4213/mzm1595

 English version: Mathematical Notes, 1997, 62:1, 104–107

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