For Ω a Polish space we consider operator semigroups on the space Cb(Ω) of bounded, continuous functions and on the space M (Ω) of bounded Borel measures. The important fact here is that the dual of Cb(Ω) with the strict topology is M (Ω). We pursue the approach via bi-continuous semigroups, but we also show that the class of bi-continuous semigroups on Cb(Ω) with respect to the compact-open to...

It is shown (Proposition (3.9)) that the asymptotic information bound which is valid for the estimation of a parameter in the structure (mixture) model remains valid in the functional model (incidental nuisance parameters) if only perturbation symmetric estimators (Deenition (3.6)) are admitted. Perturbation symmetry is a property which is closely related to permutation symmetry (Theorem (3.4))...

We extend the Theory of Computation on real numbers, continuous real functions, and bounded closed Euclidean subsets, to compact metric spaces (X, d): thereby generically including computational and optimization problems over higher types, such as the compact ‘hyper’ spaces of (i) nonempty closed subsets of X w.r.t. Hausdorff metric, and of (ii) equicontinuous functions on X . The thus obtained...

we consider the space of weakly almost periodic functions on a transformation semigroup (s, x , ?) and show that if x is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of s on x, then every continuous function on x, vanishing at infinity is weakly almost periodic. we also use a number of diverse examples to show that th...

The article investigates the local and boundary behavior of mappings with branching that satisfy inverse inequality Poletsky type. It is proved this type are logarithmically Hölder-continuous under condition function Q responsible for a distortion modulus families curves integrable. A continuous extension indicated to obtained. In addition, conditions which mentioned equicontinuous inside domai...

in this work, we define a fuzzy soft set theory and its related properties. we then define fuzzy soft aggregation operator that allows constructing more efficient decision making method. finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.

The Lie algebra of a nuclear group is a locally convex nuclear vector space. Mathematics Subject Classification (2000): 22B05, 22E65, 46Axx 1. The Lie Algebra of Abelian Topological Groups Let G be an abelian topological group. The set of all one–parameter–subgroups L(G) := {λ : R→ G : λ is a continuous homomorphism} is called the Lie algebra of G . We define addition pointwise and scalar multi...