Displaying similar documents to “Traces without maximal chains.”

On weak type inequalities for rare maximal functions in ℝⁿ

A. M. Stokolos (2006)

Colloquium Mathematicae

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The study of one-dimensional rare maximal functions was started in [4,5]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we call it "dyadic crystallization") to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.

On strong chain recurrence for maps

Katsuya Yokoi (2015)

Annales Polonici Mathematici

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This paper is concerned with strong chain recurrence introduced by Easton. We investigate the depth of the transfinite sequence of nested, closed invariant sets obtained by iterating the process of taking strong chain recurrent points, which is a related form of the central sequence due to Birkhoff. We also note the existence of a Lyapunov function which is decreasing off the strong chain recurrent set. As an application, we give a necessary and sufficient condition for the coincidence...

A remark on Vapnik-Chervonienkis classes

Agata Smoktunowicz (1997)

Colloquium Mathematicae

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We show that the family of all lines in the plane which is a VC class of index 2 cannot be obtained in a finite number of steps starting with VC classes of index 1 and applying the operations of intersection and union. This confirms a common belief among specialists and solves a question asked by several authors.