Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 124-127
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A. V. Uglanov. Four counterexamples to the Fubini theorem. Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 124-127. http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a13/
@article{MZM_1997_62_1_a13,
author = {A. V. Uglanov},
title = {Four counterexamples to the {Fubini} theorem},
journal = {Matemati\v{c}eskie zametki},
pages = {124--127},
year = {1997},
volume = {62},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a13/}
}
TY - JOUR
AU - A. V. Uglanov
TI - Four counterexamples to the Fubini theorem
JO - Matematičeskie zametki
PY - 1997
SP - 124
EP - 127
VL - 62
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a13/
LA - ru
ID - MZM_1997_62_1_a13
ER -
%0 Journal Article
%A A. V. Uglanov
%T Four counterexamples to the Fubini theorem
%J Matematičeskie zametki
%D 1997
%P 124-127
%V 62
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a13/
%G ru
%F MZM_1997_62_1_a13
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.
