相关论文: Product measures without utilizing integrals
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This result generalises the ones given up to date.
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…
We construct Markov loop measures without assuming the existence of densities for transition probabilities.
We give an example of non-translation invariant product measure obtained from two translation invariant measures, one of which is non-sigma finite. This particular example also suggests that there can be infinitely many product measures if…
I prove a theorem about iterated integrals for non-product measures in a product space. The first task is to show the existence of a family of measures on the second space, indexed by the points on of the first space (outside a negligible…
In this note, we construct an example of a sequence of $n$-fold product chains which does not display cutoff for total-variation distance neither for separation distance. In addition we show that this type of product chains necessarily…
The usual nonnegative modulus function is based on addition. A natural different modulus function on the set of positive reals is introduced. Arguments for results for series through the usual modulus function are transformed to arguments…
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.
C.Swartz' result on tensor product measures is reviewed with proofs from the scratch.
We show that for PWM-operated devices, it is possible to benefit from signal injection \emph{without an external probing signal}, by suitably using the excitation provided by the PWM itself. As in the usual signal injection framework…
Using product integrals we review the unambiguous mathematical representation of Wilson line and Wilson loop operators, including their behavior under gauge transformations and the non-abelian Stokes theorem. Interesting consistency…
We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…
We show that a probability measure is not a nontrivial free additive convolution if it puts no mass in an interval whose endpoints are atoms. The analogous results for free multiplicative convolutions are proved as well. The proofs use…
Identifying non-Markovianity with non-divisibility, we propose a measure for non-Markovinity of quantum process. Three examples are presented to illustrate the non-Markovianity, measure for non-Markovianity is calculated and discussed.…
We study few properties of square-free integers in certain equations. Using this property, we derive some infinite products in powers of square free numbers. Also, we present a method, to convert power series and trigonometric series to…
We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.
We prove in ZF that there is an inner product space, in fact, nicely definable with no orthonormal basis.
Protocols have been previously proposed to certify the presence of an entangled measurement in a fully device-independent manner. Here, I provide models for these protocols in which the claimed measurement is not entangled, and demonstrate…
The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion…
We give a new proof that the Riemann zeta function is nonzero in the half-plane $\{s\in{\mathbb C}:\sigma>1\}$. A novel feature of this proof is that it makes no use of the Euler product for $\zeta(s)$.