The notion of an almost measurable real-valued function is introduced and examined. Some properties of such functions are considered and their characterization is given. In particular, it is shown that the algebraic sum of two almost measurable functions can be a function without the property of almost measurability and that any almost measurable function becomes measurable with respect to an appropriate extension of the Lebesgue measure.
Gelbaum, B. R.
and Olmsted, J. M. H.
Counterexamples in Analysis
, Holden Day, San Francisco, 1964.
Olmsted J. M. H., '', in Counterexamples in Analysis, (1964) -.
Olmsted J. M. H.Counterexamples in Analysis1964)| false
, Solution of a problem of Banach on
-fields without continuous measures,
Bull. Acad. Polon. Sci., Ser. Sci. Math.
(1980), no. 1–2, 7–10.
Grzegorek E., 'Solution of a problem of Banach on σ-fields without continuous measures' (1980) 28Bull. Acad. Polon. Sci., Ser. Sci. Math.: 7-10.
Grzegorek E.Solution of a problem of Banach on σ-fields without continuous measuresBull. Acad. Polon. Sci., Ser. Sci. Math.198028710)| false