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Complete Boolean algebras proved to be an important tool in topology and set theory. Two of the most prominent examples are B(kappa), the algebra of Borel sets modulo measure zero ideal in the generalized Cantor space 0,1^kappa equipped with product measure, and C(kappa), the algebra of regular open sets in the space 0,1^kappa, for kappa an infinite cardinal. C(kappa) is much easier to analyse than B(kappa) : C(kappa) has a dense subset of size kappa, while the density of B(kappa) depends onarXiv:math/9502230v1 fatcat:nhysn7h6hnfxjlrnucjjtbmrlm