International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 6, Pages 353-363
doi:10.1155/S0161171202012371
Duality of measure and category in infinite-dimensional separable
Hilbert space ℓ2
Department of Higher Mathematics, Georgian Technical University, 77 Kostava Street, Tbilisi 380043, Georgia
Received 12 March 2001; Revised 16 August 2001
Copyright © 2002 Gogi Pantsulaia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We prove that an analogy of the Oxtoby duality principle is not
valid for the concrete nontrivial σ-finite Borel invariant measure and the Baire category in the classical Hilbert space ℓ2.