Pathological Linear Spaces and Submeasures.
Perimeter on Fractal sets.
Periodic multiplicative algorithms of Selmer type.
Permanence of metric fractals.
Pfeffer integrability does not imply -integrability
Physical states on quantum logics. I
Piecewise convex transformations with no finite invariant measure
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].
Piecewise Linear Wavelets on Sierpinski Gasket Type Fractals.
p-integrale selectors of multimeasures.
Poincaré inequality and Hajłasz-Sobolev spaces on nested fractals
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 inequality for some measures in Hilbert spaces and application to spectral gap for transition semigroups
Poincaré's recurrence theorem for set-valued dynamical systems
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)
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 asymptotics for the jumps of ergodic averages.
Pointwise Compact Sets of Measurable Functions.
Pointwise compactness and continuity of the integral.
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 Compactness and Weakly Compact Sets in L...
Pointwise convergence and the Wadge hierarchy
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...
Pointwise convergence of nonconventional averages
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.
Pointwise Convergence Theorems in L2 over a von Neumann Algebra.