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Piecewise convex transformations with no finite invariant measure

Tomasz Komorowski (1991)

Annales Polonici Mathematici

 Abstract. The paper concerns the problem of the existence of a finite invariant absolutely continuous measure for piecewise C 2 -regular and convex transformations T: [0, l]→[0,1]. We show that in the case when T’(0) = 1 and T"(0) exists T does not admit such a measure. This result is complementary to the ones contained in [3] and [5].

Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals

Katarzyna Pietruska-Pałuba, Andrzej Stós (2013)

Studia Mathematica

Given a nondegenerate harmonic structure, we prove a Poincaré-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajłasz-Sobolev spaces on nested fractals. In particular, we describe how the "weak"-type gradient on nested fractals relates to the upper gradient defined in the context of general metric spaces.

Poincaré's recurrence theorem for set-valued dynamical systems

Jean-Pierre Aubin, Hélène Frankowska, Andrzej Lasota (1991)

Annales Polonici Mathematici

 Abstract. The existence theorem of an invariant measure and Poincare's Recurrence Theorem are extended to set-valued dynamical systems with closed graph on a compact metric space.

Points fixes et théorèmes ergodiques dans les espaces L¹(E)

Mourad Besbes (1992)

Studia Mathematica

We prove that for each linear contraction T : X → X (∥T∥ ≤ 1), the subspace F = {x ∈ X : Tx = x} of fixed points is 1-complemented, where X is a suitable subspace of L¹(E*) and E* is a separable dual space such that the weak and weak* topologies coincide on the unit sphere. We also prove some related fixed point results.

Pointwise compactness and continuity of the integral.

G. Vera (1996)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in C(K) spaces endowed with the topology of pointwise convergence on a dense subset D in K.

Pointwise convergence and the Wadge hierarchy

Alessandro Andretta, Alberto Marcone (2001)

Commentationes Mathematicae Universitatis Carolinae

We show that if X is a Σ 1 1 separable metrizable space which is not σ -compact then C p * ( X ) , the space of bounded real-valued continuous functions on X with the topology of pointwise convergence, is Borel- Π 1 1 -complete. Assuming projective determinacy we show that if X is projective not σ -compact and n is least such that X is Σ n 1 then C p ( X ) , the space of real-valued continuous functions on X with the topology of pointwise convergence, is Borel- Π n 1 -complete. We also prove a simultaneous improvement of theorems of Christensen...

Pointwise convergence of nonconventional averages

I. Assani (2005)

Colloquium Mathematicae

We answer a question of H. Furstenberg on the pointwise convergence of the averages 1 / N ∑ n = 1 N U ⁿ ( f · R ⁿ ( g ) ) , where U and R are positive operators. We also study the pointwise convergence of the averages 1 / N ∑ n = 1 N f ( S ⁿ x ) g ( R ⁿ x ) when T and S are measure preserving transformations.

Currently displaying 21 – 40 of 148