in recent years, some statisticians have studied the signal detection problem by using the random field theory. in this paper we have considered point estimation of the gaussian scale space random field parameters in the bayesian approach. since the posterior distribution for the parameters of interest dose not have a closed form, we introduce the markov chain monte carlo (mcmc) algorithm to ap...

In this paper, we study norm almost periodic measures on locally compact Abelian groups. First, show that the periodicity of $$\mu $$ is equivalent to equi-Bohr *g$$ for all g in a fixed family functions. Then, that, absolutely continuous measures, Stepanov Radon–Nikodym density.

The Hájek-Feldman dichotomy establishes that two Gaussian measures are either mutually absolutely continuous with respect to each other (and hence there is a Radon-Nikodym density for each measure with respect to the other one) or mutually singular. Unlike the case of finite dimensional Gaussian measures, there are non-trivial examples of both situations when dealing with Gaussian stochastic pr...

The purpose of the present note is in part to extend results of Sidák [3] to cases where the measure is not finite, perhaps not even <r-finite. In particular, the conditional expectation of a random variable in Lx is obtained without the use of the Radon-Nikodym Theorem, which, indeed, does not apply with the required generality. It was found possible to extend at the same time results of [l] s...

After a review of some the main results about hyperfinite equivalence relations and their cocycles in the measured setting, we give a definition of a topological AF equivalence relation. We show that every cocycle is cohomologous to a quasi-product cocycle. We then study the problem of determining the quasi-invariant probability measures admitting a given cocycle as their Radon-Nikodym derivative.