We first establish the following Lemma which relates to the results in [1]. Lemma 1. Consider random variables X ∈ R and Y ∈ R. Let f Y |X be the Radon-Nikodym derivative of the probability measure P θ Y |X with respect to arbitrary measures QY provided that P θ Y |X QY . θ ∈ R is a parameter. f θ Y is the Radon-Nikodym derivative of probability measure P θ Y with respect to QY provided that P ...

We study harmonic analysis on cocommutative KPC-hyper-groups‎, which is a generalization of DJS-hypergroups‎, ‎introduced by Kalyuzhnyi‎, ‎Podkolzin and Chapovsky‎. ‎We prove that there is a relationship between‎ ‎the associated measures $mu$ and $gamma mu$‎, ‎where $mu$ is‎ ‎a Radon measure on KPC-hypergroup $Q$ and $gamma$ is a character on $Q$.

we study harmonic analysis on cocommutative kpc-hyper-groups‎, which is a generalization of djs-hypergroups‎, ‎introduced by kalyuzhnyi‎, ‎podkolzin and chapovsky‎. ‎we prove that there is a relationship between‎ ‎the associated measures $mu$ and $gamma mu$‎, ‎where $mu$ is‎ ‎a radon measure on kpc-hypergroup $q$ and $gamma$ is a character on $q$.

Consider a continuous function f on the real line with scalar values. It is said to have bounded support if there is a bounded interval [a, b] of real numbers such that f(x) 6= 0 implies a ≤ x ≤ b. An alternative terminology that is often used is that f is said to have compact support. Let Cc denote the vector space of continuous scalar valued functions on the real line, each of which has compa...

Abstract This paper reports a review on the relationship between seismic activity and emissions of CO 2 radon. Direct, indirect sampling methods are mainly employed to measure flux concentration in areas. The accumulation chamber technique is mostly used literature. Radon gas emission areas can be considered as short-term pre-seismic precursor. study measurement radon prior earthquakes performe...

abstract  background: the essential constituents of cements like lime, silica and alumina are derived from earth’s crust in which radioactive elements like uranium, thorium etc are also present in varying amounts almost everywhere. these two elements are considered as the parent elements of uranium and thorium radioactive decay series in which radon and thoron are produced respectively as decay...

Exposure to radon is the second leading cause of lung cancer after smoking. Radon is an odorless, tasteless and invisible gas produced by the decay of naturally occurring uranium in soil and water. The amount of radon in the air is measured in "picocuries per liter of air," or "pCi/L." There are many kinds of low-cost "do-it-yourself" radon test kits you can get through the mail and in some har...

Let X be a Banach space and (Ω,Σ, λ) be a finite measure space, 1 ≤ p < ∞. It is shown that L(λ,X) has the Near Radon-Nikodym property if and only if X has it. Similarly if E is a Köthe function space that does not contain a copy of c0, then E(X) has the Near Radon-Nikodym property if and only if X does.

We propose a new method to measure the (222)Rn concentration in a closed bore-hole and to use the results for estimation of the diffusion parameter and the average radium content of the surrounding geological formations. In a closed bore-hole, only several meters from the surface, the radon concentration is rather constant (in the +/-15% range) under different meteorological conditions. The inf...