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arXiv · 1103.0247

Measurability in C(2^k) and Kunen cardinals

Antonio Avilés·Grzegorz Plebanek·José Rodríguez
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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.

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Antonio Avilés, Grzegorz Plebanek, José Rodríguez. 2011-10-31. Measurability in C(2^k) and Kunen cardinals. https://arxiv.org/abs/1103.0247

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