Pathological Linear Spaces and Submeasures.
N.J. Kaiton, James W. Roberts (1983)
Mathematische Annalen
Piero D'Ancona, Andrea Braides (1991)
Manuscripta mathematica
Schweiger, Fritz (2005)
Integers
Tintarev, Kyril (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Jiří Jarník, Jaroslav Kurzweil (1994)
Czechoslovak Mathematical Journal
J. Gunson (1972)
Annales de l'I.H.P. Physique théorique
Tomasz Komorowski (1991)
Annales Polonici Mathematici
Abstract. The paper concerns the problem of the existence of a finite invariant absolutely continuous measure for piecewise -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].
Robert S. Strichartz (1997)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
Alò, Richard A., De Korvin, Andre, Roberts, Charles E.jun. (1979)
International Journal of Mathematics and Mathematical Sciences
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.
Giuseppe Da Prato (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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.
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.
Catuogno, P. J., Ferrando, S. E. (2001)
The New York Journal of Mathematics [electronic only]
D.H. Fremlin (1975)
Manuscripta mathematica
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.
Surjit Singh Khurana (1981)
Mathematische Zeitschrift
Alessandro Andretta, Alberto Marcone (2001)
Commentationes Mathematicae Universitatis Carolinae
We show that if is a separable metrizable space which is not -compact then , the space of bounded real-valued continuous functions on with the topology of pointwise convergence, is Borel--complete. Assuming projective determinacy we show that if is projective not -compact and is least such that is then , the space of real-valued continuous functions on with the topology of pointwise convergence, is Borel--complete. We also prove a simultaneous improvement of theorems of Christensen...
I. Assani (2005)
Colloquium Mathematicae
We answer a question of H. Furstenberg on the pointwise convergence of the averages , where U and R are positive operators. We also study the pointwise convergence of the averages when T and S are measure preserving transformations.
Eva Hensz, Ryszard Jajte (1986)
Mathematische Zeitschrift