  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.
