Results 41 to 50 of about 69,299 (185)

Iterated Function Systems in Mixed Euclidean and p-adic Spaces

, 2006
We investigate graph-directed iterated function systems in mixed Euclidean and p-adic spaces. Hausdorff measure and Hausdorff dimension in such spaces are defined, and an upper bound for the Hausdorff dimension is obtained.
Sing, Bernd
core   +2 more sources

Nonstandard Measure Theory-Hausdorff Measure [PDF]

Proceedings of the American Mathematical Society, 1977
In this paper it is shown that the Hausdorff measures λ t {\lambda ^t} for t ∈ [ 0 , ∞ ) t \in [0,\infty ) can be simultaneously represented as ∗ ^\ast finite counting measures in an appropriate ...
openaire   +2 more sources

The hausdorff metric and measurable selections

Topology and its Applications, 1985
We contruct measurable selections for closed set-valued maps into arbitrary complete metric spaces. We do not need to make any separability assumptions. We view the set-valued maps as point-valued maps into the hyperspace and our measurability assumptions are the usual kinds of measurability of point-valued maps in this setting.
Karel Prikry, C. J. Himmelberg, F. S. Van Vleck   +2 more
openaire   +2 more sources

Hausdorff Outer Measures and the Representation of Coherent Upper Conditional Previsions by the Countably Additive Möbius Transform

Fractal and Fractional
This paper explores coherent upper conditional previsions, a class of nonlinear functionals that generalize expectations while preserving consistency properties.
Serena Doria
doaj   +1 more source

Infinite System of Differential Equations in Some Spaces

Abstract and Applied Analysis, 2012
The first measure of noncompactness was defined by Kuratowski in 1930 and later the Hausdorff measure of noncompactness was introduced in 1957 by Goldenštein et al.
M. Mursaleen, Abdullah Alotaibi
doaj   +1 more source

Problem with two-point conditions for parabolic equation of second order on time

Karpatsʹkì Matematičnì Publìkacìï, 2014
The  correctness of the problem with two-point conditions on time variable and Dirichlet-type conditions  on spetial coordinates for the linear  parabolic equations are established.
M.M. Symotyuk, I.R. Tymkiv
doaj   +1 more source

How to extend Carath\'eodory's theorem to lattice-valued functionals

Results in Nonlinear Analysis, 2020
Substituting in the definition of outer measure the addition with the maximum (or the supremum, or the join) operation we obtain a new set function called retuo measure. It is proved that every retuo measure is an outer measure.
Nutefe Kwami Agbeko
doaj  

On the dimension of a certain measure in the plane [PDF]

, 2013
We study the Hausdorff dimension of a measure related to a positive weak solution of a certain partial differential equation in a simply connected domain in the plane.
Dedicated John, L. Lewis, Murat Akman
core  

On the Billingsley dimension of Birkhoff average in the countable symbolic space

Comptes Rendus. Mathématique, 2020
We compute a lower bound of Billingsley–Hausdorff dimension, defined by Gibbs measure, of the level set related to Birkhoff average in the countable symbolic space $\mathbb{N}^{\mathbb{N}}$.
Attia, Najmeddine, Selmi, Bilel
doaj   +1 more source

Exact Hausdorff measure on the boundary of a Galton--Watson tree

, 2007
A necessary and sufficient condition for the almost sure existence of an absolutely continuous (with respect to the branching measure) exact Hausdorff measure on the boundary of a Galton--Watson tree is obtained.
Watanabe, Toshiro
core   +1 more source