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On convergence in capacity

Published online by Cambridge University Press:  17 April 2009

Burnett Meyer
Burnett Meyer
Affiliation:
Department of Mathematics, University of Colorado, Boulder, Colorado, USA.
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The (logarithmic) capacity or transfinite diameter is originally defined for compact sets in the complex plane. An extension may be made by defining the capacity of a given arbitrary set in the plane as the supremum of the capacities of all compact sets contained in the given set. Convergence in capacity is defined analogously to convergence in measure. It is shown in this paper that properties of convergence in capacity are also analogous to those of convergence in measure.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 1 , February 1976 , pp. 1 - 5
Copyright
Copyright © Australian Mathematical Society 1976

References

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