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Displaying similar documents to “Integrability and L 1 -convergence of Rees-Stanojević sums with generalized semi-convex coefficients of non-integral orders”

Entropy and growth of expanding periodic orbits for one-dimensional maps

A. Katok, A. Mezhirov (1998)

Fundamenta Mathematicae

Similarity:

Let f be a continuous map of the circle S 1 or the interval I into itself, piecewise C 1 , piecewise monotone with finitely many intervals of monotonicity and having positive entropy h. For any ε > 0 we prove the existence of at least e ( h - ε ) n k periodic points of period n k with large derivative along the period, | ( f n k ) ' | > e ( h - ε ) n k for some subsequence n k of natural numbers. For a strictly monotone map f without critical points we show the existence of at least ( 1 - ε ) e h n such points.

Analytic determinacy and 0# A forcing-free proof of Harrington’s theorem

Ramez Sami (1999)

Fundamenta Mathematicae

Similarity:

We prove the following theorem: Given a⊆ω and 1 α < ω 1 C K , if for some η < 1 and all u ∈ WO of length η, a is Σ α 0 ( u ) , then a is Σ α 0 . We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: Σ 1 1 -Turing-determinacy implies the existence of 0 .

Sierpiński's hierarchy and locally Lipschitz functions

Michał Morayne (1995)

Fundamenta Mathematicae

Similarity:

Let Z be an uncountable Polish space. It is a classical result that if I ⊆ ℝ is any interval (proper or not), f: I → ℝ and α < ω 1 then f ○ g ∈ B α ( Z ) for every g B α ( Z ) Z I if and only if f is continuous on I, where B α ( Z ) stands for the αth class in Baire’s classification of Borel measurable functions. We shall prove that for the classes S α ( Z ) ( α > 0 ) in Sierpiński’s classification of Borel measurable functions the analogous result holds where the condition that f is continuous is replaced by the condition that f is locally...