Related papers: On control measures of multimeasures

We give several structural results concerning the Lipschitz-free spaces $\mathcal F(M)$, where $M$ is a metric space. We show that $\mathcal F(M)$ contains a complemented copy of $\ell_1(\Gamma)$, where $\Gamma=\text{dens}(M)$. If $\mathcal…

It is proven that if $G$ is a finite group, then $G^\omega$ has $2^{\mathfrak c}$ dense nonmeasurable subgroups. Also, other examples of compact groups with dense nonmeasurable subgroups are presented.

Let $M_R$ be a module and $\sigma$ an endomorphism of $R$. Let $m\in M$ and $a\in R$, we say that $M_R$ satisfies the condition $\mathcal{C}_1$ (respectively, $\mathcal{C}_2$), if $ma=0$ implies $m\sigma(a)=0$ (respectively, $m\sigma(a)=0$…

We show that for every compact 3-manifold $M$ there exists an open subset of $\diff ^1(M)$ in which every generic diffeomorphism admits uncountably many ergodic probability measures which are hyperbolic while their supports are disjoint and…

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X --> X such that the set A = {x in X : ||R^n(x)|| --> infinity} is non-empty and nowhere dense in X. Moreover, if…

We develop aspects of geometric control theory on Lie groups G which may be infinite dimensional, and on smooth G-manifolds M modelled on locally convex spaces. As a tool, we discuss existence and uniqueness questions for differential…

A compact space X is I-favorable if, and only if X can be representing as a limit of $\sigma$-complete inverse system of compact metrizable spaces with skeletal bonding maps.

A set X subseteq R is strongly meager if for every measure zero set H, X+H not= R. Let SM denote the collection of strongly meager sets. We show that assuming CH, SM is not an ideal.

We prove in a direct fashion that a multidimensional probability measure is determinate if the higher dimensional analogue of Carleman's condition is satisfied. In that case, the polynomials, as well as certain proper subspaces of the…

In this paper we study sufficient conditions for an operator to have an almost-invariant half-space. As a consequence, we show that if $X$ is an infinite-dimensional complex Banach space then every operator $T\in\mathcal{L}(X)$ admits an…

Given any positive integers $m$ and $d$, we say the a sequence of points $(x_i)_{i\in I}$ in $\mathbb R^m$ is {\em Lipschitz-$d$-controlling} if one can select suitable values $y_i\; (i\in I)$ such that for every Lipschitz function…

Consider a sequence of minimal varieties M_i in a Riemannian manifold N such that the boundary measures are uniformly bounded on compact sets. Let Z be the set of points at which the areas of the M_i blow up. We prove that Z behaves in some…

Let $E$ be one of the spaces $C(K)$ and $L_1$, $F$ be an arbitrary Banach space, $p>1,$ and $(X,\sigma)$ be a space with a finite measure. We prove that $E$ is isometric to a subspace of the Lebesgue-Bochner space $L_p(X;F)$ only if $E$ is…

Hare, Mendivil, and Zuberman have recently shown that if $X$ is a compact subset of the reals and of non-zero Assouad dimension $\dim_A X$, then for all $s>\dim_A X$, $X$ supports measures with Assouad dimension $s$. We generalise this…

We give an alternative proof of a fact that a finite continuous non-decreasing submodular set function on a measurable space can be expressed as a supremum of measures dominated by the function, if there exists a class of sets which is…

We prove that if $X$ is a real Banach space, with $\dim X\geq 3$, which contains a subspace of codimension 1 which is 1-complemented in $X$ and whose group of isometries is almost transitive then $X$ is isometric to a Hilbert space. This…

Let $M$ be a compact manifold of dimension at least 2. If $M$ admits a minimal homeomorphism then $M$ admits a minimal noninvertible map.

We study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space $X$. In particular we give an example of a reflexive $X$ so that all spreading models of $X$ contain $\ell_1$…

We prove that for some manifolds $M$ the set of robustly transitive partially hyperbolic diffeomorphisms of $M$ with one-dimensional nonhyperbolic centre direction contains a $C^1$-open and dense subset of diffeomorphisms with nonhyperbolic…

In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded…