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 – 12 of 12

Showing per page

Egoroff, σ, and convergence properties in some archimedean vector lattices

A. W. Hager, J. van Mill (2015)

Studia Mathematica

An archimedean vector lattice A might have the following properties: (1) the sigma property (σ): For each a ₙ n ∈ ℕ c o n A ⁺ there are λ ₙ n ∈ ℕ ⊆ ( 0 , ∞ ) and a ∈ A with λₙaₙ ≤ a for each n; (2) order convergence and relative uniform convergence are equivalent, denoted (OC ⇒ RUC): if aₙ ↓ 0 then aₙ → 0 r.u. The conjunction of these two is called strongly Egoroff. We consider vector lattices of the form D(X) (all extended real continuous functions on the compact space X) showing that (σ) and (OC ⇒ RUC) are equivalent, and equivalent...

Entropy on effect algebras with the Riesz decomposition property I: Basic properties

Antonio Di Nola, Anatolij Dvurečenskij, Marek Hyčko, Corrado Manara (2005)

Kybernetika

We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.

Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps

Petr Holický (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove an abstract version of the Kuratowski extension theorem for Borel measurable maps of a given class. It enables us to deduce and improve its nonseparable version due to Hansell. We also study the ranges of not necessarily injective Borel bimeasurable maps f and show that some control on the relative classes of preimages and images of Borel sets under f enables one to get a bound on the absolute class of the range of f. This seems to be of some interest even within separable spaces.

Currently displaying 1 – 12 of 12

Page 1