Related papers: Product measures without utilizing integrals
We provide a new technique to prove Ornstein's non-inequalities for derivatives with some geometrical dependence on their indexes.
We give a probabilistic characterization of the set of measures that can be represented by the matrix product ansatz. By suitably enlarging the state space, we show that a probability measure can be described in terms of non negative…
We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes' theorem.
Quantum measurements on a two-level system can have more than two independent outcomes, and in this case, the measurement cannot be projective. Measurements of this general type are essential to an operational approach to quantum theory,…
We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…
We show that the perturbation of a Palm measure by an independent process with stationary increments remains a Palm measure.
We establish estimates for the number of ways to represent any reduced residue class as a product of a prime and an integer free of small prime factors. Our best results is conditional on the Generalised Riemann hypothesis (GRH). As a…
We construct surface measures associated to Gaussian measures in separable Banach spaces, and we prove several properties including an integration by parts formula.
Equations are ubiquitous in most mathematical activities. Nevertheless, in this paper it is shown how to do standard mathematics without any equation at all. More than that, it is proven there is a foundational framework for standard…
Additive manufacturing has the potential to become a standard method for manufacturing products, and product information is indispensable for the item distribution system. While most products are given barcodes to the exterior surfaces,…
Measurement-based quantum computation is a novel model of quantum computing where universal quantum computation can be done with only local measurements on each particle of a quantum many-body state, which is called a resource state. One…
This paper is devoted to study some expressions of the type $\prod_{p} p^{\lfloor\frac{x}{f(p)}\rfloor}$, where $x$ is a nonnegative real number, $f$ is an arithmetic function satisfying some conditions, and the product is over the primes…
A slight modification to Halmos' definition of product of measures yields a uniquely characterized associative product. The operation applies to arbitrary (not necessarily $\sigma-$finite) measures and is consistent with the Fubini--Tonelli…
We introduce a method for evaluating integrals in geometric calculus without introducing coordinates, based on using the fundamental theorem of calculus repeatedly and cutting the resulting manifolds so as to create a boundary and allow for…
In ``interaction free'' measurements, one typically wants to detect the presence of an object without touching it with even a single photon. One often imagines a bomb whose trigger is an extremely sensitive measuring device whose presence…
In this article we propose a general method of obtaining infinite sums of products with functions that count patterns in numbers.
A novel manifestation of nonlocality of quantum mechanics is presented. It is shown that it is possible to ascertain the existence of an object in a given region of space without interacting with it. The method might have practical…
We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of these operators as…
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.
Interaction-free measurement and quantum interrogation schemes can help in the detection of particles without interacting with them in a classical sense. We present a density matrix study of a quantum interrogation system designed for…