Extension of real-valued α-additive set 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.
Finitely additive invariant measures. I
Finitely additive invariant measures. II
Finitely subadditive outer measures, finitely superadditive inner measures and their measurable sets.
Fonction convexe d'une mesure et applications
Formes linéaires positives et mesures
Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schrödinger Cauchy problems.
From finite to countable additivity
Generalized fractional integral operators on weak Choquet spaces over quasi-metric measure spaces
We prove the boundedness of the generalized fractional maximal operator and the generalized fractional integral operator on weak Choquet spaces with respect to Hausdorff content over quasi-metric measure spaces.
Generalized Vitali systems of uniform type
Generic sets in definably compact groups
A subset X of a group G is called left genericif finitely many left translates of X cover G. Our main result is that if G is a definably compact group in an o-minimal structure and a definable X ⊆ G is not right generic then its complement is left generic. Among our additional results are (i) a new condition equivalent to definable compactness, (ii) the existence of a finitely additive invariant measure on definable sets in a definably compact group G in the case where G = *H...
Hereditary measurable sets and universal measure
How subadditive are subadditive capacities?
Subadditivity of capacities is defined initially on the compact sets and need not extend to all sets. This paper explores to what extent subadditivity holds. It presents some incidental results that are valid for all subadditive capacities. The main result states that for all hull-additive capacities (a class that contains the strongly subadditive capacities) there is countable subadditivity on a class at least as large as the universally measurable sets (so larger than the analytic sets).
Integration on generalized measure spaces
Interpolation of quasicontinuous functions
If C is a capacity on a measurable space, we prove that the restriction of the K-functional to quasicontinuous functions f ∈ QC is equivalent to . We apply this result to identify the interpolation space .
Kelly's theorem from the duality of LP and Tychonoff's theorem
-improving properties of measures of positive energy dimension
A measure is called -improving if it acts by convolution as a bounded operator from to for some q > p. Positive measures which are -improving are known to have positive Hausdorff dimension. We extend this result to complex -improving measures and show that even their energy dimension is positive. Measures of positive energy dimension are seen to be the Lipschitz measures and are characterized in terms of their improving behaviour on a subset of -functions.
Lattice normality and outer measures.
Lattice separation and measures.