Vol. 65, No. 2, 1976

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The absolute Baire property

John C. Morgan, II

Vol. 65 (1976), No. 2, 421–436

In earlier papers the author has formulated an axiomatic foundation for a general theory of point sets, one of whose purposes is the unification of analogous theorems concerning Baire category and Lebesgue measure. Within this context, a method is given in the present paper for unifying the Baire property in the restricted sense and absolute measurability on the real line.

That absolute measurability is the appropriate measure-theoretic analogue of the Baire property in the restricted sense was suggested by E. Marczewski in a classical paper in 1937, after he had established the Baire property (in the wide sense) and Lebesgue measurability as analogous concepts.

Mathematical Subject Classification 2000
Primary: 54H05
Received: 19 April 1976
Published: 1 August 1976
John C. Morgan, II