Graham-Rothschild parameter words and measurable partitions

Abstract

Generalizing earlier results of Moran and Strauss (Mathematika 27, 1980, 213–244) and of Carlson and Simpson (Adv. in Math. 53, 1984, 265–290) it was shown in Prömel and Voigts (Trans. Amer. Math. Soc. 291, 1985, 198–201) that Baire sets ofk-parameter words are Ramsey. Motivated by the “duality” between category and measure, we investigate in this paper measurable sets ofk parameter words. We show that measurable sets of ascendingk-parameter words are Ramsey, whereas in general measurable sets ofk-parameter words fail to be Ramsey.

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Prömel, H.J., Voigt, B. Graham-Rothschild parameter words and measurable partitions. Combinatorica 11, 253–259 (1991). https://doi.org/10.1007/BF01205077

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