Lutian Zhao UID: 661622198 The Duistermaat-Heckman theorems concern the measure associated to moment map of a torus action of symplectic manifold. Typically, this name refers to two theorems, one is called the ”Duistermaat-Heckman measure", which says that ”the Radon-Nikodym derivative is piecewise polynomial", the definition of each terms will be introduced later. The second one is called ”Dui...

We introduce length dilatation structures on metric spaces, tempered dilatation structures and coherent projections and explore the relations between these objects and the Radon-Nikodym property and Gamma-convergence of length functionals. Then we show that the main properties of sub-riemannian spaces can be obtained from pairs of length dilatation structures, the first being a tempered one and...

In the framework of 5] we prove regularity of invariant measures for a class of Ornstein{Uhlenbeck operators perturbed by a drift which is not necessarily bounded or Lipschitz continuous. Regularity here means that is absolutely continuous with respect to the Gaussian invariant measure of the unperturbed operator with the square root of the Radon{Nikodym density in the corresponding Sobolev spa...

We consider two singular limits: a fast reaction limit with non-monotone nonlinearity and regularization of the forward-backward diffusion equation. derive pointwise identities satisfied by Young measure generated these problems. As result, we obtain an explicit formula for even without non-degeneracy assumption used in previous works. The main new idea is application Radon–Nikodym theorem to d...

It is well-known that there is an intimate connection between the RadonNikodym property and martingale convergence in a Banach space. This connection can be "localized" to a closed bounded convex subset of a Banach space. In this paper we are interested primarily in this connection for a bounded convex set which is not closed. If C is a bounded convex set in a locally convex space, C is said to...