Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that each these measures some similar or property. Such combined with metric to yield a which are respect multiple

We introduce a new quantum Gromov-Hausdorff distance between C∗-algebraic compact quantum metric spaces. Because it is able to distinguish algebraic structures, this new distance fixes a weakness of Rieffel’s quantum distance. We show that this new quantum distance has properties analogous to the basic properties of the classical Gromov-Hausdorff distance, and we give criteria for when a parame...

In this paper, we study the geometry of non-Archimedean Gromov-Hausdorff metric. This is the first part of our series work, which we try to establish some facts about the counterpart of Gromov-Hausdorff metric in the non-Archimedean spaces. One of the motivation of this work is to find some implied relations between this geometry and number theory via p-adic analysis, so that we can use the for...

Preface In this monograph various notions related to metric spaces are considered, including Hausdorff-type measures and dimensions, Lipschitz mappings, and the Hausdorff distance between nonempty closed and bounded subsets of a metric space. Some familiarity with basic topics in analysis such as Riemann integrals, open and closed sets, and continuous functions is assumed, as in [60, 100, 187],...

In a Euclidean space , the Lebesgue-Stieltjes integral of set-valued stochastic processes d R       , 0, t F F t T    with respect to real valued finite variation process       , 0, t A t T   t is defined directly by employing all integrably bounded selections instead of taking the decomposable closure appearing in some existed references. We shall show that this kind of integr...

Given a bounded metric space X, the set of closed sets of X supports a metric, the Hausdorff metric. Whether X is bounded or not, there is a compact, locally compact topology on the space of closed sets. If A,B ⊂ X are closed sets, define their Hausdorff distance dH(A,B) to be the number inf { r | B is in the r − neighborhood of A andA is in the r − neighborhood of B }. We can say this more pre...