Extension on the fuzzy integral based on -decomposable measure.
Extension theorems (vector measures on quantum logics)
Extensions de systèmes dynamiques par des endomorphismes de groupes compacts
Extensions of additive mappings
Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps
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.
Extensions of Cocycles for Hyperfinite Actions and Applications.
Extensions of invariant measures on Euclidean spaces
Extensions of measurable functions
Extensions of positive operators and extreme points. I
Extensions of positive operators and extreme points. II
Extensions of positive operators and extreme points. III
Extensions of positive operators and extreme points. IV
Extensions of probability-preserving systems by measurably-varying homogeneous spaces and applications
We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such extensions rests on a simple notion of 'direct integral' for a 'measurable family' of homogeneous spaces, which has a number of precedents in older literature. The main contribution of the present paper is the systematic development of a formalism for handling such extensions,...
Extensions of semigroup valued, finitely additive measures.
Extensions of set functions.
We establish a necessary and sufficient condition for a function defined on a subset of an algebra of sets to be extendable to a positive additive function on the algebra. It is algo shown that this condition is necessary and sufficient for a regular function defined on a regular subset of the Borel algebra of subsets of a given compact Hausdorff space to be extendable to a measure.
Extraction of a “good” subsequence from a bounded sequence of integrable functions.
Extremal preimage measures and measurable weak sections
Extremal solutions of a general marginal problem
The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.
Extreme essential derivatives of Borel and Lebesgue measurable functions
Extreme topological measures
It has been an open question since 1997 whether, and under what assumptions on the underlying space, extreme topological measures are dense in the set of all topological measures on the space. The present paper answers this question. The main result implies that extreme topological measures are dense on a variety of spaces, including spheres, balls and projective planes.