On a Lusin theorem for capacities

A Quantitative Lusin Theorem for Functions in BV

We extend to the BV case a measure theoretic lemma previously proved by DiBenedetto, Gianazza and Vespri ([1]) in W 1,1 loc . It states that if the set where u is positive occupies a sizable portion of a open set E then the set where u is positive clusters about at least one point of E. In this note we follow the proof given in the Appendix of [3] so we are able to use only a 1−dimensional Poin...

A Saitô–tomita–lusin Theorem for Jb∗-triples and Applications

A theorem of Lusin is proved in the non-ordered context of JB∗-triples. This is applied to obtain versions of a general transitivity theorem and to deduce refinements of facial structure in closed unit ballls of JB∗-triples and duals.

Varadhan’s theorem for capacities

Varadhan’s integration theorem, one of the corner stones of large-deviation theory, is generalized to the context of capacities. The theorem appears valid for any integral that obeys four linearity properties. We introduce a collection of integrals that have these properties. Of one of them, known as the Choquet integral, some continuity properties are established as well.

A constructive version of the Lusin Separation Theorem

Bayes' Theorem for Choquet Capacities

We give an upper bound for the posterior probability of a measurable set A when the prior lies in a class of probability measures 9. The bound is a rational function of two Choquet integrals. If g; is weakly compact and is closed with respect to majorization, then the bound is sharp if and only if the upper prior probability is 2-alternating. The result is used to compute-bounds for several set...