Let X be a compact Hausdorff space. In this work we translate partial actions of to on some hyperspaces determined by X, gives an endofunctor 2- in the category spaces which generates monad category. Moreover, structural relations between θ and 2θ as well their corresponding globalizations are established.

order that a (real) sequence #, may have the representation /~,=S f dx(t), 0 where X(t) is a function of bounded variation in [0, 1]. HARDY [3] outlines the proof of HAUSDORFF; several alternate proofs of the result of HAUSDORFF are known (see for instance WIDOER [14] and LORENTZ [8]). One of these alternate proofs makes use of the uniform approximation of functions continuous in [0, 1 ] by the...

Following Lutz’s approach to effective (constructive) dimension, we define a notion of dimension for individual sequences based on Schnorr’s concept(s) of randomness. In contrast to computable randomness and Schnorr randomness, the dimension concepts defined via computable martingales and Schnorr tests coincide, i.e. the Schnorr Hausdorff dimension of a sequence always equals its computable Hau...

Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset with a nontrivial non-Hausdorff topology. Their ability to reproduce important topological information of the continuum has been the main motivation for the...

We give a necessary and sufficient condition on a Randers space for the existence of a measure for which Shen’s S-curvature vanishes everywhere. Moreover, such a measure coincides with the Busemann-Hausdorff measure up to a constant multiplication.

We consider all the transcendental meromorphic functions from the class S whose Julia set is a Jordan curve. We show that then the Julia set is either a straight line or its Hausdorff dimension is strictly larger than 1.

Following a recent paper [10] we show that the finiteness of square function associated with the Riesz transforms with respect to Hausdorff measure H implies that s is integer.

Gromov-Hausdorff convergence is an important tool in comparison Riemannian geometry. Given a sequence of Riemannian manifolds of dimension n with Ricci curvature bounded from below, Gromov’s precompactness theorem says that a subsequence will converge in the pointed Gromov-Hausdorff topology to a length space [G-99, Section 5A]. If the sequence has bounded sectional curvature, then the limit wi...

In their classic paper, S. Orey and S.J. Taylor compute the Hausdorff dimension of the set of points at which the law of the iterated logarithm fails for Brownian motion. By introducing “fast sets”, we describe a converse to this problem for fractional Brownian motion. Our result is in the form of a limit theorem. From this, we can deduce refinements to the aforementioned dimension result of Or...

This paper describes a new method of image pattern recognition based on the Hausdorff Distance. The technique looks for similarities between a given pattern and its possible representations within an image. This method performs satisfactorily when confronted to image perturbations or partial occlusions. An extension of the classical Hausdorff Distance technique chooses the best candidate among ...