Integral representation of certain linear functionals

Integral Representation of Continuous Comonotonically Additive Functionals

In this paper, I first prove an integral representation theorem: Every quasi-integral on a Stone lattice can be represented by a unique uppercontinuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinite...

Linear Functionals on Certain Banach Spaces

Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure Spaces

This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined through relaxation, and it defines a Radon measure on the space. For the singular part of the functional, we get the expected integral representation with respect to the variation measure. A new feature is that i...

Integral Representation of Abstract Functionals of Autonomous Type

In this work we extend the results of [2] to a family of abstract functionals of autonomous type satisfying suitable locality and additivity properties, and general integral growth conditions of superlinear type. We single out a condition which is necessary and sufficient in order for a functional of this class to admit an integral representation, and sufficient as well to have an integral repr...

Multiple integral representation for functionals of Dirichlet processes

We point out that a proper use of the Hoeffding–ANOVA decomposition for symmetric statistics of finite urn sequences, previously introduced by the author, yields a decomposition of the space of square-integrable functionals of a Dirichlet–Ferguson process, written L(D), into orthogonal subspaces of multiple integrals of increasing order. This gives an isomorphism between L(D) and an appropriate...