Related papers: On vector measures with values in $c_0(\kappa)$

In [8] the second and third authors showed that if the least inaccessible cardinal is the least measurable cardinal, then there is an inner model with $o(\kappa)\geq2$. In this paper we improve this to $o(\kappa)\geq\kappa+1$ and show that…

$\Sigma^1_3$-absoluteness for ccc forcing means that for any ccc forcing $P$, ${H_{\omega_1}}^V \prec_{\Sigma_2}{H_{\omega_1}}^{V^P}$. "$\omega_1$ inaccessible to reals" means that for any real $r$, ${\omega_1}^{L[r]}<\omega_1$. To measure…

We investigate the cofinality of the strong measure zero ideal for $\kappa$ inaccessible, and show that it is independent of the size of $2^\kappa$.

For d nonpolar compact sets K_1,...,K_d in the complex plane, d admissible weights Q_1,...,Q_d, and a positive semidefinite d x d interaction matrix C with no zero column, we define natural discretizations of the associated weighted vector…

Let $\mu$ be a self-similar measure satisfying the finite type condition. It is known that the set of attainable local dimensions for such a measure is a union of disjoint intervals, where some intervals may be degenerate points. Despite…

Let $\mathcal{M}=\{m_\lambda\}_{\lambda\in\Lambda}$ be a separating family of lattice seminorms on a vector lattice $X$, then $(X,\mathcal{M})$ is called a multi-normed vector lattice (or MNVL). We write $x_\alpha \xrightarrow{\mathrm{m}}…

We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a…

We investigate the properties of linear primitive liftings $\rho\colon \mathcal{L}^p(\mu)\to \mathcal{L}^p(\mu)$ for probability spaces $(X,\Sigma,\mu)$, which are linear maps selecting a representative from each class for almost everywhere…

Let $\mathcal{H}$ denote a connected component of a stratum of translation surfaces. We show that the Siegel-Veech transform of a bounded compactly supported function on $\mathbb{R}^2$ is in $L^2(\mathcal{H}, \mu)$, where $\mu$ is Lebesgue…

Let $L$ be a countable language. We characterize, in terms of definable closure, those countable theories $\Sigma$ of $\mathcal{L}_{\omega_1, \omega}(L)$ for which there exists an $S_\infty$-invariant probability measure on the collection…

In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continous convex functions on a vector space ${\bf R}^m$ and vector-valued functions in a weakly compact subset of a…

Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\bf R$.…

Nonnegative measures that are solutions to a transport equation with continuous coefficients have been widely studied. Because of the low regularity of the associated vector field, there is no natural flow since nonuniqueness of integral…

This article studies the harmonicity of vector fields on Riemannian manifolds, viewed as maps into the tangent bundle equipped with a family of Riemannian metrics. Geometric and topological rigidity conditions are obtained, especially for…

It is well known that real measures on the circle are characterized by their Herglotz transform, an analytic function in the unit disc. Invariance of the measure under N-multiplication translates into a functional equation for the Herglotz…

Let L_1 be the predual of a von Neumann algebra with a finite faithful normal trace. We show that a bounded sequence in L_1 converges to 0 in measure if and only if each of its subsequences admits another subsequence which converges to 0 in…

We construct a measure on omega-one^2 over the ground model in the forcing extension of a measure algebra, and investigate when measure theoretic properties of some measurable colouring of omega-one^2 imply the existence of an uncountable…

We prove that there exists uncountably many pairwise disjoint open subsets of the Gelfand space of the measure algebra on any locally compact non-discrete abelian group which shows that this space is not separable (in fact, we prove this…

Let $\mathbb{S} \subset \mathbb{C}$ be the circle in the plane, and let $\Omega: \mathbb{S} \to \mathbb{S}$ be an odd bi-Lipschitz map with constant $1+\delta_\Omega$, where $\delta_\Omega>0$ is small. Assume also that $\Omega$ is twice…

Answering some of the main questions from [MR13], we show that whenever $\kappa$ is a cardinal satisfying $\kappa^{< \kappa} = \kappa > \omega$, then the embeddability relation between $\kappa$-sized structures is strongly invariantly…