Related papers: A note on product of measures
We consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability…
In 2014, Ibrahim M Alabdulmohsin wrote a paper called "Summability Calculus" where he developed a method to generalize sigma notation to non-integer upper bounds. His paper included a theorem, known as Theorem 6.1.1 (denoted here as Lemma…
In this paper we give an axiomatic characterization of the cap product in the Hochschild theory of associative unital algebras which are projective over a commutative unital ring. We also give an interpretation of the cap product with…
The regularized product of the Fibonacci numbers is evaluated.
Previous derivations of the sum and product rules of probability theory relied on the algebraic properties of Boolean logic. Here they are derived within a more general framework based on lattice theory. The result is a new foundation of…
We prove in this note that there is, for some foliated bundles, a bijective correspondance between Garnett's harmonic measures and measures on the fiber that are stationary for some probability measure on the holonomy group. As a…
Let $M$ be an $\aleph_0$-categorical structure and assume that $M$ has no algebraicity and has weak elimination of imaginaries. Generalizing classical theorems of de Finetti and Ryll-Nardzewski, we show that any ergodic,…
We give a new categorical approach to the Halmos-von Neumann theorem for actions of general topological groups. As a first step, we establish that the categories of topological and measure-preserving irreducible systems with discrete…
Adopting a purely group-theoretical point of view, we consider the star product of functions which is associated, in a natural way, with a square integrable (in general, projective) representation of a locally compact group. Next, we show…
By means of a modified hypervirial theorem we derive simple expressions for the integrals of products of Airy functions. Present results contain earlier ones as particular cases.
The direct product of two Fibonacci tilings can be described as a genuine stone inflation rule with four prototiles. This rule admits various modifications, which lead to 48 different inflation rules, known as the direct product variations.…
A result of Nymann is extended to show that a positive $\sigma$-finite measure with range an interval is determined by its level sets. An example is given of two finite positive measures with range the same finite union of intervals but…
In the article a new measure in infinite dimensional unite cube different from the Haar or product measures is constructed. Some differences between introduced measure and the product measure are discussed.
Relative to a given factoring of the Hilbert space, the decomposition of an operator into a convex sum of products over sets of distinct 1-projectors, one set linearly independent, is unique.
In this paper we show that a new type of products hoops can be defined which, in the case of finite hoops, can describe an arbitrary hoop $\mathbf A$ as the product of its arbitrary filter $F$ and the corresponding homomorphic image…
The aim of this paper is to study ultralimits of pointed metric measure spaces (possibly unbounded and having infinite mass). We prove that ultralimits exist under mild assumptions and are consistent with the pointed measured…
In this work we discuss Dirichlet products evaluated at Fibonacci numbers. As first applications of the results we get a representation of Fibonacci numbers in terms of Euler's totient function, an upper bound on the number of primitive…
We show in this paper that representations of a finite product of categories satisfying certain combinatorial conditions have finite Castelnuovo-Mumford regularity if and only if they are presented in finite degrees, and hence the category…
A formulation of anomalies in terms of star products is suggested which promises insight from an alternative and unifying point of view.
One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…