Random finite set provides a rigorous foundation for optimal Bayes multi-target filtering. The major hurdle faced in Bayes multi-target filtering is the inherent computational intractability. Even the Probability Hypothesis Density (PHD) filter, which propagates only the first moment (or PHD) instead of the full multi-target posterior, still involves multiple integrals with no closed forms. In ...

We study actions of discrete groups on Hilbert C-modules induced from topological actions on compact Hausdorff spaces. We prove that amenable actions give rise to proper affine isometric actions, provided there is a quasiinvariant measure which is sufficiently close to being invariant in a certain sense. This provides conditions on non-amenability of actions. The notion of amenability of group ...

Radon is a naturally occurring radioactive gas found in varying amounts in all soils. Therefore, it is very important to study radon emanation from different soils in different circumstances; especially, in green houses which widely used to propagate and cultivate of plants. In greenhouses radon comes from either soil or the substances which make suitable flooring in the greenhouse. Radon and i...

After describing the main characteristics of grain-size curves, we recall previous results about Principal Components Analysis of absolutely continuous measures, in connection with grain-size curves analysis. This method simultaneously takes into account a chosen reference probability (r.p.) μ (associated with a Radon-Nikodym derivation operator), and the imposed sampling mesh Tp. The point is ...

Let E be a Banach space. There are several natural ways in which any polynomial P ∈ P(E) can be extended to P̃ ∈ P(E), in such a way that the extension mapping is continuous and linear (see, for example, [6]). Taking the double transpose of the extension mapping P → P̃ yields a linear, continuous mapping from P(E) into P(E). Further, since P(E) is a dual space, it follows that there is a natural ...

We prove that there exists a diiusion process whose invariant measure is the three-dimensional polymer measure. The diiusion is constructed by means of the theory of Dirichlet forms on innnite-dimensional state spaces. We prove the closabi-lity of the appropriate pre-Dirichlet form which is of gradient type, using a general closability result by two of the authors. This result does not require ...

We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [HK96]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of exam...

We show that a separable Banach space has the RadonNikodym Property (RNP) if and only if it is isomorphic to the limit of an inverse system, V1 ← V2 ← . . . ← Vk ← . . . , where the Vi’s are finite dimensional Banach spaces, and the bonding maps Vk−1 ← Vk are quotient maps. We also show that the inverse system can be chosen to be a good finite dimensional approximation (GFDA), a notion introduc...

A Theorem of Lyapunov states that the range R(μ) of a non–atomic vector measure μ is compact and convex. In this paper we give a condition to detect the dimension of the extremal faces of R(μ) in terms of the Radon–Nikodym derivative of μ with respect to its total variation |μ|: namely R(μ) has an extremal face of dimension less or equal to k if and only if the set (x1, . . . , xk+1) such that ...

We establish several deep existence criteria for conditional expectations on von Neumann algebras, and then apply this theory to develop a noncommutative of representing measures characters function algebra. Our main cycle results describes what may be understood as ‘noncommutative Hoffman-Rossi theorem’ giving the weak* continuous measures’ so-called D -characters. These also viewed ‘module’ H...