[Banach] Abstract of a paper by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez

This is an announcement for the paper "Measurability in C(2^k) and Kunen cardinals" by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez.

Abstract: A cardinal k is called a Kunen cardinal if the sigma-algebra on k x k generated by all products AxB, coincides with the power set of k x k. For any cardinal k, let C(2^k) be the Banach space of all continuous real-valued functions on the Cantor cube 2^k. We prove that k is a Kunen cardinal if and only if the Baire sigma-algebra on C(2^k) for the pointwise convergence topology coincides with the Borel sigma-algebra on C(2^k) for the norm topology. Some other links between Kunen cardinals and measurability in Banach spaces are also given.

Archive classification: math.FA

Mathematics Subject Classification: 28A05, 28B05

Submitted from: avileslo@um.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1103.0247

or

http://arXiv.org/abs/1103.0247