Weak Compactness and Tightness of Subsets of M(X).
Weak convergence in Hoffmann-Jorgensen sense
Weak Convergence of Measures.
Weak Fubini theorems for the Dobrakov integral
Weak integrals defined on Euclidean n-space
Weak regularity of probability measures.
Weakly compactly generated Frechet spaces.
When is a Riesz distribution a complex measure?
Let be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by . I give an elementary proof of the necessary and sufficient condition for to be a locally finite complex measure (= complex Radon measure).
When is the Haar measure a Pietsch measure for nonlinear mappings?
We show that, as in the linear case, the normalized Haar measure on a compact topological group G is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of C(G). This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed.
Which Bernoulli measures are good measures?
For measures on a Cantor space, the demand that the measure be "good" is a useful homogeneity condition. We examine the question of when a Bernoulli measure on the sequence space for an alphabet of size n is good. Complete answers are given for the n = 2 cases and the rational cases. Partial results are obtained for the general cases.
Which moments of a logarithmic derivative imply quasiinvariance.
Why minimax is not that pessimistic
In nonparametric statistics a classical optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this point of view can be subject to controversy as it requires to look for the worst behavior of an estimation procedure in a given space. The purpose of this paper is to introduce a new criterion based on generic behavior of estimators. We are here interested in the rate of convergence obtained with some classical estimators on almost every, in the sense...