Related papers: A counterexample regarding an equivalence relation…

We prove an explicit finite-sample version of the Borel--Cantelli lemma under $m$-dependence. Given any $m$-dependent sequence of events $(A_k)_{1\leq k\leq N}$, we show that \[ \mathbb{P}\Bigl(\bigcup_{k=1}^N A_k\Bigr) \ge 1 -…

Combining Kasparov's theorem of Voiculesu and Cuntz's description of $KK$-theory in terms of quasihomomorphisms, we give a simple construction of the Kasparov product. This will be used in a more general context of locally convex algebras…

We prove that in the Laver model for the consistency of the Borel's conjecture, the product of any two $H$-separable spaces is $M$-separable.

A ``self--similar'' example is constructed that shows that a conjecture of N. U. Arakelyan on the order of decrease of deficiencies of an entire function of finite order is not true.

In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and…

The statistics behind Bell's inequality is demonstrated to allow a Kolmogorovian (i.e. classical) model of probabilities that recovers the quantum covariance.

In this note, we show that there is some counterexample for isoperimetric inequality if the condition $(\phi')^2-\phi"\phi\leq 1$ does not hold in warped product space.

This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.

We give necessary and sufficient conditions for Borel measures to satisfy the inequality introduced by Komisarski, Rajba (2018). This inequality is a generalization of the convex order inequality for binomial distributions, which was proved…

Markov categories are a recent category-theoretic approach to the foundations of probability and statistics. Here we develop this approach further by treating infinite products and the Kolmogorov extension theorem. This is relevant for all…

We provide a proof of a conjecture in (Bailey, Borwein, Borwein, Crandall 2007) on the existence and form of linear recursions for moments of powers of the Bessel function $K_0$.

This paper develops aspects of cosheaf theory on rigid analytic spaces, and demonstrates a sheaf-cosheaf Verdier duality equivalence theorem for overconvergent sheaves on separated, paracompact spaces, analogous to Jacob Lurie's treatment…

Lindel\"of spaces are studied in any basic Topology course. However, there are other interesting covering properties with similar behaviour, such as almost Lindel\"of, weakly Lindel\"of, and quasi-Lindel\"of, that have been considered in…

Refining some results of S. S. Dragomir, several new reverses of the triangle inequality in inner product spaces are obtained.

Consider a measured equivalence relation acting on a bundle of hyperbolic metric spaces by isometries. We prove that every aperiodic hyperfinite subequivalence relation is contained in a {\em unique} maximal hyperfinite subequivalence…

Let $D$ and $E$ be subspaces of the tensor product of the $m$ and $n$ dimensional complex spaces, with codimensions $k$ and \ell$, respectively. We show that if $k+\ell<m+n-2$ then there must exist a product vector in $D$ whose partial…

We analyze a definition of product of Banach spaces that is naturally associated by duality with an abstract notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different…

We consider various notions of equivalence in the space of bounded operators on a Hilbert space, in particular modulo finite rank, modulo Schatten $p$-class, and modulo compact. Using Hjorth's theory of turbulence, the latter two are shown…

We give an example for the Kuznetsov-Shinder conjecture, with infinitely many non-isomorphic D-equivalent and L-equivalent varieties.

In this paper, we construct a compact subset of the real plane whose path-connectedness equivalence relation is Borel bireducible to a nonsmooth hyperfinite Borel equivalence relation. This answers a question of \cite{bec98}.