"Paradoxe" Zerlegung Euklidischer Räume.
Parameterized curve as attractors of some countable iterated function systems
In this paper we will demonstrate that, in some conditions, the attractor of a countable iterated function system is a parameterized curve. This fact results by generalizing a construction of J. E. Hutchinson [Hut81].
Partial measures.
Partial variational principle for finitely generated groups of polynomial growth and some foliated spaces
We generalize the notion of topological pressure to the case of a finitely generated group of continuous maps and introduce group measure entropy. Also, we provide an elementary proof that any finitely generated group of polynomial growth admits a group invariant measure and show that for a group of polynomial growth its measure entropy is less than or equal to its topological entropy. The dynamical properties of groups of polynomial growth are reflected in the dynamics of some foliated spaces.
Partition of nondenumerable closed sets of reals
Partitioned iterated function systems with division and a fractal dependence graph in recognition of 2D shapes
One of the approaches in pattern recognition is the use of fractal geometry. The property of self-similarity of fractals has been used as a feature in several pattern recognition methods. All fractal recognition methods use global analysis of the shape. In this paper we present some drawbacks of these methods and propose fractal local analysis using partitioned iterated function systems with division. Moreover, we introduce a new fractal recognition method based on a dependence graph obtained from...
Partitions of pairs of reals
Pasting together Julia sets: a worked out example of mating.
Pathological Linear Spaces and Submeasures.
Perimeter on Fractal sets.
Permanence of metric fractals.
Pfeffer integrability does not imply -integrability
Piecewise Linear Wavelets on Sierpinski Gasket Type Fractals.
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.
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 density topology
The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density...
Poissonian products of random weights: uniform convergence and related measures.