Related papers: The class S as an ME invariant

It is shown to be consistent with set theory that the uniformity invariant for Lebesgue measure is strictly greater than the corresponding invariant for Hausdorff r-dimensional measure where 0<r<1.

We show that the class $\mathscr{B}$, of discrete groups which satisfy the conclusion of Popa's Cocycle Superrigidity Theorem for Bernoulli actions, is invariant under measure equivalence. We generalize this to the setting of discrete…

In this paper, we discuss a longstanding conjecture of Greenberg in the Iwasawa theory of elliptic curves. Greenberg's conjecture states that if $E/\mathbb{Q}$ is an elliptic curve with good ordinary reduction at $p$, and $E[p]$ is…

In this paper we study the class $\mathcal{E}_{m}(\Omega)$ of $m-$subharmonic functions introduced by Lu in \cite{L1}. We prove that the convergence in $m-$capacity implies the convergence of the associated Hessian measure for functions…

We formulate a criterion for the existence of an invariant measure for a Feller semigroup defined on a metric space with the e-property for bounded continuous functions and use it to prove the asymptotic stability of a semigroup satisfying…

Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…

In this note we give a fairly direct proof of a recent theorem of Gorska, Lemanczyk and de la Rue which characterises the class of measure preserving transformations that are disjoint from every ergodic measure preserving transformation.…

A survey of recent results concerning cardinal invariants of measure and category. Submitted as a chapter of the upcoming Handbook of Set Theory.

Assuming that Iwasawa's $\mu_{K/k}$-invariant vanishes, we prove the 'main conjecture' of equivariant Iwasawa theory, at odd prime numbers $l$, for arbitrary extensions $K/k$ of totally real number fields, up to its uniqueness assertion.

We study the Benjamin-Ono equation, posed on the torus. We prove that an infinite sequence of weighted gaussian measures, constructed in our previous work, are invariant by the flow of the equation. These measures are supported by Sobolev…

In a recent publication [PRL 111, 160405 (2013)] we proved a version of Heisenberg's error-disturbance tradeoff. This result was in apparent contradiction to claims by Ozawa of having refuted these ideas of Heisenberg. In a direct reaction…

We will prove the equivariant version of Smale's transversality theorem: suppose that the compact Lie-group G acts on the compact differentiable manifold M on which an invariant Morse-function f and an invariant vector field X are given so…

In this paper, we prove Smale's mean value conjecture by making use of quasiconformal deformations and holomorphic motions.

We study invariant measures of continuous contact model in small dimensional spaces ($d =1,2$). Under general conditions we prove that in the critical regime this system has the one-parameter set of invariant measures parametrized by the…

For a maximal abelian subalgebra $A\subset M$ in a finite von Neumann algebra, we consider an invariant due to Takesaki which is an equivalence relation on a standard probability space. We give several characterization of this invariant and…

We prove existence of a non-round Einstein metric $g$ on $S^{12}$ that is invariant under the usual cohomogeneity one action of $\mathsf{O}(3)\times\mathsf{O}(10)$ on $S^{12}\subset \mathbb{R}^{13}= \mathbb{R}^3\oplus \mathbb{R}^{10}$. The…

Let $\mathcal{S}$ be an integrable Pfaffian system. If it is invariant under a transversally free infinitesimal action of a finite dimensional real Lie algebra $g$ and consequently invariant under the local action of a Lie group $G$, we…

We consider a nonstationary sequence of independent random isometries of a compact metrizable space. Assuming that there are no proper closed subsets with deterministic image we establish a weak-* convergence to the unique invariant under…

We prove a positive mass theorem for continuous Riemannian metrics in the Sobolev space $W^{2, n/2}_{\mathrm{loc}}(M)$. We argue that this is the largest class of metrics with scalar curvature a positive a.c. measure for which the positive…

We present a direct confirmation of the validity of the equivalence principle for unstructured test bodies in scalar tensor gravity. Our analysis is complementary to previous approaches and valid for a large class of scalar-tensor theories…