Related papers: Transverse invariant measures extends to the ambie…

In this manuscript, a conformally invariant theory of gravitation in the context of metric measure space is studied. The proposed action is invariant under both diffeomorphism and conformal transformations. Using the variational method, a…

For a compact riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Holder bicontinuous homeomorphism. However, the riemannian metric defines a…

We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…

We study unimodular measures on the space $\mathcal M^d$ of all pointed Riemannian $d$-manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups…

We construct surface measures associated to Gaussian measures in separable Banach spaces, and we prove several properties including an integration by parts formula.

We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…

I provide a proof of the existence of absolutely continuous invariant measures (and study their statistical properties) for multidimensional piecewise expanding systems with not necessarily bounded derivative or distortion. The proof uses…

We prove that multiple-recurrence and polynomial-recurrence of invertible infinite measure preserving transformations are both properties which pass to extensions.

We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant…

It is known that Iterated Function Systems generated by orientation preserving homeomorphisms of the unit interval admit a unique invariant measure on $(0,1)$. The setup for this result is the positivity of Lyapunov exponents at both fixed…

Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on…

In the paper we are dealing with metric measure spaces of diameter at most one and of total measure one. Gromov introduced the sampling compactification of the set of these spaces. He asked whether the metric measure space invariants extend…

We consider a class of non-locally compact groups on which one may define a left-invariant, finitely additive measure taking values in some finitely generated extension of the field $\mathbb{R}$ of real numbers. In particular, we recover…

We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…

We investigate extension of a measure to a very general set of undetermined structure. Structure may be imposed on this set in special cases

In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…

A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.

Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a measure can be defined as the supremum, resp. infimum, of…

Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…

This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…