All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 14 of 14

Showing per page

The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces

S. Gabriyelyan, J. Kąkol, G. Plebanek (2016)

Studia Mathematica

Following Banakh and Gabriyelyan (2016) we say that a Tychonoff space X is an Ascoli space if every compact subset of C k ( X ) is evenly continuous; this notion is closely related to the classical Ascoli theorem. Every k ℝ -space, hence any k-space, is Ascoli. Let X be a metrizable space. We prove that the space C k ( X ) is Ascoli iff C k ( X ) is a k ℝ -space iff X is locally compact. Moreover, C k ( X ) endowed with the weak topology is Ascoli iff X is countable and discrete. Using some basic concepts from probability theory and...

The homology of spaces of simple topological measures

Ø. Johansen, A. B. Rustad (2003)

Fundamenta Mathematicae

The simple topological measures X* on a q-space X are shown to be a superextension of X. Properties inherited from superextensions to topological measures are presented. The homology groups of various subsets of X* are calculated. For a q-space X, X* is shown to be a q-space. The homology of X* when X is the annulus is calculated. The homology of X* when X is a more general genus one space is investigated. In particular, X* for the torus is shown to have a retract homeomorphic to an infinite product...

The (sub/super)additivity assertion of Choquet

Heinz König (2003)

Studia Mathematica

The assertion in question comes from the short final section in Theory of capacities of Choquet (1953/54), in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this operation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and similarly for superadditivity. His treatment of this point was more like an outline, and his proof limited to a rather narrow special case. Thus the proper...

The uniqueness of Haar measure and set theory

Piotr Zakrzewski (1997)

Colloquium Mathematicae

Let G be a group of homeomorphisms of a nondiscrete, locally compact, σ-compact topological space X and suppose that a Haar measure on X exists: a regular Borel measure μ, positive on nonempty open sets, finite on compact sets and invariant under the homeomorphisms from G. Under some mild assumptions on G and X we prove that the measure completion of μ is the unique, up to a constant factor, nonzero, σ-finite, G-invariant measure defined on its domain iff μ is ergodic and the G-orbits of all points...

Two problems on doubling measures.

Robert Kaufman, Jang-Mei Wu (1995)

Revista Matemática Iberoamericana

Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?

Currently displaying 1 – 14 of 14

Page 1