A Measure Space Without the Strong Lifting Property.
A note on almost strong liftings
Let be a locally compact space. A lifting of where is a positive measure on , is almost strong if for each bounded, continuous function , and coincide locally almost everywhere. We prove here that the set of all measures on such that there exists an almost strong lifting of is a band.
A Remark on a Theorem of Losert.
A survey on lifting in measure theory
Can we assign the Borel hulls in a monotone way?
A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/ hull to every negligible/measurable subset of [0,1]? Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent....
Category bases.
Desintegration and compact measures.
Diferenciación de medidas vectoriales en semi-μ-espacios de Lusin.
Easure and Integration in the Alternative set Theory
Equivariant measurable liftings
We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Möbius group of the projective line. Since the general proof is very simple but not explicit, we also provide a much more explicit lifting for semisimple Lie groups acting on their Furstenberg boundary, using unrestricted Fatou convergence. This setting is relevant to -cocycles for characteristic classes.
Homeomorphic measures on products of intervals.
Measures on Product Spaces and the Existence of Strong Baire Liftings.
Non existence de relèvement pour certaines mesures finiement additives et retractés de ...N.
On idempotent Liftings
On lifting quasi-Radon measures.
On products of admissible liftings and densities.
On strong liftings for projective limits
We discuss the permanence of strong liftings under the formation of projective limits. The results are based on an appropriate consistency condition of the liftings with the projective system called "self-consistency", which is fulfilled in many situations. In addition, we study the relationship of self-consistency and completion regularity as well as projective limits of lifting topologies.
On the lifting of invariant measures
Product liftings and densities with lifting invariant and density invariant sections
Given two measure spaces equipped with liftings or densities (complete if liftings are considered) the existence of product liftings and densities with lifting invariant or density invariant sections is investigated. It is proved that if one of the marginal liftings is admissibly generated (a subclass of consistent liftings), then one can always find a product lifting which has the property that all sections determined by one of the marginal spaces are lifting invariant (Theorem 2.13). For a large...
Radon-Nikodym property
For a Banach space and a probability space , a new proof is given that a measure , with , has RN derivative with respect to iff there is a compact or a weakly compact such that is a finite valued countably additive measure. Here we define where is a finite disjoint collection of elements from , each contained in , and satisfies . Then the result is extended to the case when is a Frechet space.