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Abstract
The paper deals with the category analogue of a density point and a density topology (with respect to a Lebesgue measure) on the real line which is different from the mathcal {I}-density topology considered in Poreda et al. (Fundam Math 125:167–173, 1985; Comment Math Univ Carol 26:553–563, 1985). This topology called the intensity topology, manifests several properties analogous to that of mathcal {I}-density topology, but there are also differences. The class of function which are continuous as functions from {mathbb {R}} equipped with an intensity topology to {mathbb {R}} equipped with the natural topology is included in the first class of Baire Darboux functions.
Highlights
In [8] one can find a characterization of a Lebesgue density point which uses only the σ -ideal of nullsets
In this paper we shall formulate another characterization of a Lebesgue density point, again not using a Lebesgue measure but only the σ -ideal of nullsets
This characterization leads again to a definition of category density point, which is, not equivalent to I-density and to a category density topology, which is different from the I-density topology
Summary
In [8] one can find a characterization of a Lebesgue density point which uses only the σ -ideal of nullsets. In this paper we shall formulate another characterization of a Lebesgue density point, again not using a Lebesgue measure but only the σ -ideal of nullsets. This characterization leads again to a definition of category density point, which is, not equivalent to I-density and to a category density topology, which is different from the I-density topology. In the sequel L will denote the σ -algebra of Lebesgue measurable sets on the real line, N —the σ -ideal of nullsets, B—the σ -algebra of sets having the Baire property,
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