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On Helly's principle for metric semigroup valued BV mappings to two real variables

Published online by Cambridge University Press:  17 April 2009

M. Balcerzak ,
S. A. Belov  and
V. V. Chistyakov
M. Balcerzak
Affiliation:
Institute of Mathematics, Lódź Technical University, al. Politechniki 11, I-2, 90–924 Lódź, and Faculty of Mathematics, Lódź University, ul. Banacha 22, 90–238 Lódź, Poland e-mail: mbalce@krysia.uni.lodz.pl
S. A. Belov
Affiliation:
Department of Mathematics, University of Nizhny Novgorod, Gagarin Avenue 23, Nizhny Novgorod 603950, Russia e-mail: belov@vmk.unn.ru
V. V. Chistyakov
Affiliation:
Department of Mathematics, University of Nizhny Novgorod, Gagarin Avenue 23, Nizhny Novgorod 603950, Russia e-mail: chistya@mm.unn.ac.ru chistya@mm.unn.ru
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We introduce a concept of metric space valued mappings of two variables with finite total variation and define a counterpart of the Hardy space. Then we establish the following Helly type selection principle for mappings of two variables: Let X be a metric space and a commutative additive semigroup whose metric is translation invariant. Then an infinite pointwise precompact family of X-valued mappings on the closed rectangle of the plane, which is of uniformly bounded total variation, contains a pointwise convergent sequence whose limit is a mapping with finite total variation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 2 , October 2002 , pp. 245 - 257
Copyright
Copyright © Australian Mathematical Society 2002

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