Displaying similar documents to “Remarks on differential concomitants of densities”

On relations between f -density and ( R ) -density

Václav Kijonka (2007)

Acta Mathematica Universitatis Ostraviensis

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In this paper it is discus a relation between f -density and ( R ) -density. A generalization of Šalát’s result concerning this relation in the case of asymptotic density is proved.

Category theorems concerning Z-density continuous functions

K. Ciesielski, L. Larson (1991)

Fundamenta Mathematicae

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The ℑ-density topology T ℑ on ℝ is a refinement of the natural topology. It is a category analogue of the density topology [9, 10]. This paper is concerned with ℑ-density continuous functions, i.e., the real functions that are continuous when the ℑ-densitytopology is used on the domain and the range. It is shown that the family C ℑ of ordinary continuous functions f: [0,1]→ℝ which have at least one point of ℑ-density continuity is a first category subset of C([0,1])= f: [0,1]→ℝ: f is continuous...

Asymptotic density, computable traceability, and 1-randomness

Uri Andrews, Mingzhong Cai, David Diamondstone, Carl Jockusch, Steffen Lempp (2016)

Fundamenta Mathematicae

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Let r ∈ [0,1]. A set A ⊆ ω is said to be coarsely computable at density r if there is a computable function f such that {n | f(n) = A(n)} has lower density at least r. Our main results are that A is coarsely computable at density 1/2 if A is computably traceable or truth-table reducible to a 1-random set. In the other direction, we show that if a degree a is hyperimmune or PA, then there is an a-computable set which is not coarsely computable at any positive density.

Regular sets and conditional density: an extension of Benford's law

Rita Giuliano Antonini, Georges Grekos (2005)

Colloquium Mathematicae

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We give an extension of Benford's law (first digit problem) by using the concept of conditional density, introduced by Fuchs and Letta. The main tool is the notion of regular subset of integers.