Abstract
We prove some consequences of various measurability hypotheses. Especially, we establish that the measurability of Σ 12 sets implies that Σ 12 sets have the property of Baire.
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References
T. Bartoszynski,Additivity of measure implies additivity of category, to appear.
A. W. Miller,Additivity of measure implies dominating reals, Proc. Am. Math. Soc., to appear.
J. C. Oxtoby,Measure and Category, Springer-Verlag, New York, 1971.
J. Raisonnier,A mathematical proof of S. Shelah's theorem on the measure problem and related results, Isr. J. Math.48 (1984), 48–56.
J. Rainsonnier and J. Stern,Mesurabilité et propriété de Baire, C. R. Acad. Sci. Paris, Sér. A296 (1983), 323–326.
A. Renyi,Calcul des probabilités, Dunod, Paris, 1966.
S. Shelah,Can you take Solovay's inaccessible away, Isr. J. Math.48 (1984), 1–47.
R. M. Solovay,A model of set theory in which every set of reals is Lebesgue measurable, Ann. of Math.92 (1970), 1–56.
J. Stern,Some measure theoretic results in effective descriptive set theory, Isr. J. Math.20 (1975), 97–100.
J. Stern,Regularity properties of definable sets of reals, Ann. Math. Logic. to appear.
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Raisonnier, J., Stern, J. The strength of measurability hypotheses. Israel J. Math. 50, 337–349 (1985). https://doi.org/10.1007/BF02759764
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DOI: https://doi.org/10.1007/BF02759764