Extension of null-additive set functions on algebra of subsets.
Extension of real-valued α-additive set functions
Extension theorems (vector measures on quantum logics)
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 invariant measures on Euclidean spaces
Extensions of measurable functions
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 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
Extremely non-normal continued fractions