Measurability and the abstract Baire property
- 20 Downloads
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.
KeywordsPositive Measure Ordinal Number Category Base Hausdorff Measure Continuum Hypothesis
Unable to display preview. Download preview PDF.
- Rogers C.A.,Hausdorff Measures, Cambridge 1970.Google Scholar
- Sierpinski W.,Hypothése du Continu, New York 1956.Google Scholar
- Szpilrajn E., (Marczewski),Sur un ensemble non mesurable de M. Sierpinski. Sprawozdania z posiedzén Towarzystwa Naukowego Warszawskiego, Wydzial III (Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III),24 (1931), 78–85.Google Scholar