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Almost all normal sets are strictly normal

Published online by Cambridge University Press:  17 April 2009

Alexander J. Zaslavski
Alexander J. Zaslavski
Affiliation:
Department of Mathematics, The Technion-Israel Institute of Technology, 3200 Haifa, Israel, e-mail: ajzasl@tx.technion.ac.il
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We consider the space Sn of all nonempty bounded closed normal subsets of the cone where is the set of all vectors x ∈ Rn with nonnegative coordinates. We equip the space Sn with the Hausdorff metric and show that most elements of Sn are, in fact, strictly normal. More precisely, we show that the complement of the collection of all stricly normal elements of Sn is a σ-porous subset of Sn.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 151 - 159
Copyright
Copyright © Australian Mathematical Society 2004

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