A generalization of the density topology

Rok, strany: 2006, 37 - 47

In the paper we introduce a notion of $f$-density point of the measurable set on the real line. This notion is a generalization of Lebesgue density and also of $ψ$-density which was introduced in [S. J. Taylor: On strengthening the Lebesgue density theorem, Fund. Math. 46 (1959) 395–315]. We examine basic properties of an $f$-density and of a topology generated by it. Moreover, we investigate relationships between $f$-density and Lebesgue density and between $f$-densities for different functions $f$.

ISO 690:

Filipczak, M., Filipczak, T. 2006. A generalization of the density topology. In Tatra Mountains Mathematical Publications, vol. 34, no.2, pp. 37-47. 1210-3195.

APA:

Filipczak, M., Filipczak, T. (2006). A generalization of the density topology. Tatra Mountains Mathematical Publications, 34(2), 37-47. 1210-3195.