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

  • M. Balcerzak (a1), S. A. Belov (a2) and V. V. Chistyakov (a3)

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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.

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

  • M. Balcerzak (a1), S. A. Belov (a2) and V. V. Chistyakov (a3)

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