Let (Ω, d) be a metric space where Ω is a set with positive and finite Hausdorff outer measure in its Hausdorff dimension and let B be a partition of Ω. The coherent upper conditional prevision defined as the Choquet integral with respect to its associated Hausdorff outer measure is proven to satisfy the disintegration property and the conglomerative principle on every partition.

metric spaces and approximating fixed points of a pair of contractive type mappings M. Abbas, M. Jovanović, S. Radenović University of Belgrade School of Electrical Engineering http://www.etf.bg.ac.rs JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, Vol. 13, No. 2, pp. 243253, Jan, 2011 References: Abstract: Recently, Chao Wang, Jinghao Zhu, Boško Damjanović, Liang-gen Hu [Approximating fixe...

We show that a topological space is hereditarily irresolvable if and only if it is Hausdorff-reducible. We construct a compact irreducible T1-space and a connected Hausdorff space, each of which is strongly irresolvable. Furthermore, we show that the three notions of scattered, Hausdorff-reducible, and hereditarily irresolvable coincide for a large class of spaces, including metric, locally com...

The Hausdorff–Alexandroff Theorem states that any compact metric space is the continuous image of Cantor’s ternary set C. It is well known that there are compact Hausdorff spaces of cardinality equal to that of C that are not continuous images of Cantor’s ternary set. On the other hand, every compact countably infinite Hausdorff space is a continuous image of C. Here we present a compact counta...

The theory of Hausdorff dimension provides a general notion of the size of a set in a metric space. We define Hausdorff measure and dimension, enumerate some techniques for computing Hausdorff dimension, and provide applications to self-similar sets and Brownian motion. Our approach follows that of Stein [4] and Peres [3].

We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...

In this paper, we introduce the notion of weak $psi$-quasi contraction in generalized metric spaces and using this notion we obtain conditions for the existence of fixed points of a self map in $D$-complete generalized metric spaces. We deduce some corollaries from our result and provide examples in support of our main result.

We introduce and study (metrically) quarter-stratifiable spaces and then apply them to generalize Rudin and Kuratowski-Montgomery theorems about the Baire and Borel complexity of separately continuous functions. The starting point for writing this paper was the desire to improve the results of V.K. Maslyuchenko et al. [MMMS], [MS], [KM], [KMM] who generalized a classical theorem of W.Rudin [Ru]...

We prove that each analytic set in R contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitzlike mappings of separable metric s...

We review basics concerning metric spaces from a contemporary viewpoint, and prove the important Baire category theorem, for both complete metric spaces and locally compact Hausdorff [1] spaces.