Related papers: Tangent measures of non-doubling measures
Non-homogeneous self-similar measures are generically absolute continuous in the domain of parameters for which the similarity dimension is larger than one, see \cite{[SSS]}. Using certain algebraic curves we construct here exceptional…
We give a universal recipe for constructing nonlinear entanglement witnesses able to detect non-classical correlations in arbitrary systems of distinguishable and/or identical particles for an arbitrary number of constituents. The…
We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S-M. Ngai and Y. Wang. While recently there has been much…
We show that for any set $A\subseteq [0,1]^n$ with $\text{Vol}(A)\ge 1/2$ there exists a line $\ell $ such that the one-dimensional Lebesgue measure of $\ell \cap A$ is at least $\Omega ( n^{1/4} )$. The exponent $1/4$ is tight. More…
In this paper, we establish spectral inequalities on measurable sets of positive Lebesgue measure for the Stokes operator, as well as an observability inequalities on space-time measurable sets of positive measure for non-stationary Stokes…
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the…
In this paper we solve the Monge problem on infinite dimensional Hilbert space endowed with a suitable Gaussian measure, that satisfies the Lebesgue differentiation theorem.
This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation…
We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.
We study behavior of a measure on $[0,\infty)$ by considering its Laplace transform. If it is possible to extend the Laplace transform to a complex half-plane containing the imaginary axis, then the exponential decay of the tail of the…
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…
We present a single inequality as the necessary and sufficient condition for two unsharp observables of a two-level system to be jointly measurable in a single apparatus and construct explicitly the joint observables. A complementarity…
We build a toy model of differential geometry on the real line, which includes derivatives of the second order. Such construction is possible only within the framework of noncommutative geometry. We introduce the metric and briefly discuss…
We construct surface measures associated to Gaussian measures in separable Banach spaces, and we prove several properties including an integration by parts formula.
Starting from gauged N=8 supergravity in three dimensions we construct actions for multiple membranes by taking the limit to global supersymmetry for different choices of the embedding tensor. This provides a general framework that…
Measures are introduced to quantify the degree of superposition in mixed states with respect to orthogonal decompositions of the Hilbert space of a quantum system. These superposition measures can be regarded as analogues to entanglement…
It is shown that any transverse invariant measure of a foliated space can be considered as a measure on the ambient space.