Applications of outer measures to separation properties of lattices and regular or -smooth measures.
Approximating pavings and construction of measures
Arzela - Ascoli's Theorem for Riemann - Integrable Functions on Compact Spaces.
Bessel potentials in Orlicz spaces.
It is shown that Bessel potentials have a representation in term of measure when the underlying space is Orlicz. A comparison between capacities and Lebesgue measure is given and geometric properties of Bessel capacities in this space are studied. Moreover it is shown that if the capacity of a set is null, then the variation of all signed measures of this set is null when these measures are in the dual of an Orlicz-Sobolev space.
Capacitary Orlicz spaces, Calderón products and interpolation
These notes are devoted to the analysis on a capacity space, with capacities as substitutes of measures of the Orlicz function spaces. The goal is to study some aspects of the classical theory of Orlicz spaces for these spaces including the classical theory of interpolation.
Capacity of Sets and Uniform Distribution of Sequences.
Capacity relations in a flat quadrilateral.
Cardinality of some convex sets and of their sets of extreme points
We show that the cardinality of a compact convex set W in a topological linear space X satisfies the condition that . We also establish some relations between the cardinality of W and that of extrW provided X is locally convex. Moreover, we deal with the cardinality of the convex set E(μ) of all quasi-measure extensions of a quasi-measure μ, defined on an algebra of sets, to a larger algebra of sets, and relate it to the cardinality of extrE(μ).
Characterizations of outer measures associated with lattice measures.
Choquetova teorie kapacit
Comment on "On some statistical paradoxes and non-conglomerability" by Bruce Hill.
Those who follow Harold Jeffreys in using improper priors together with likelihoods to determine posteriors have thought of the improper measures as probability measures of a deviant sort. This is a mistake. Probability measures are finite measures. Improper distributions generate σ-finite measures. (...)
Compactness and extreme points of the set of quasi-measure extensions of a quasi-measure [Book]
Conditional symmetries of stable measures on
Construction of aggregation operators: new composition method
A new construction method for aggregation operators based on a composition of aggregation operators is proposed. Several general properties of this construction method are recalled. Further, several special cases are discussed. It is also shown, that this construction generalizes a recently introduced twofold integral, which is exactly a composition of the Choquet and Sugeno integral by means of a min operator.
Construction of Measure from Semialgebra of Sets1
In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore, we...
Continuity and Extension of Valuations
Correction to the paper "Two classes of measures''
Coverable standard measures with the chain condition and the Lebesgue decomposition
Daniell-Greco-Stone representation type theorem for autocontinuous from above functionals.
Darboux property of measures and contents