1,359 research outputs found
Convergence results for conditional expectations
Let E,F be two Polish spaces and [Xn,Yn],[X,Y] random variables with values in E×F (not necessarily defined on the same probability space). We show some conditions which are sufficient in order to assure that, for each bounded continuous function f on E×F, the conditional expectation of f(Xn,Yn) given Yn converges in distribution to the conditional expectation of f(X,Y) given Y
On the isoperimetric problem with double density
In this paper we consider the isoperimetric problem with double density in an
Euclidean space, that is, we study the minimisation of the perimeter among
subsets of with fixed volume, where volume and perimeter are
relative to two different densities. The case of a single density, or
equivalently, when the two densities coincide, has been well studied in the
last years; nonetheless, the problem with two different densities is an
important generalisation, also in view of applications. We will prove the
existence of isoperimetric sets in this context, extending the known results
for the case of single density.Comment: 19 pages, 1 figure. A subscript is missing in the hypothesis of
Theorem A and related Lemmas in the published version. This version contains
the correct statement
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