Measurability and the abstract Baire property
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Within an abstract theory of point sets the author has successfully unified a substantial number of the analogous theorems concerning Lebesgue measure and Baire category. It has been shown that the Lebesgue measurable sets coincide with the sets having the abstract Baire property with respect to the family of all closed sets of positive Lebesgue measure and the question was raised in  whether the sets measurable with respect to certain Hausdorff measures were the same as the sets having the abstract Baire property with respect to the family of all closed sets of positive Hausdorff measure. In this article we establish a general theorem which, under the assumption of the continuum hypothesis, gives an affirmative answer to this question.
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