Let ~ and m be excessive measures for a right Markov process X and let Q~ and Qm be the associated stationary Kuznetsov processes. We show that if ~ and m are harmonic, then Q~ ~ Qm if and only if ~ is quasi-bounded by m in the sense that ~ = where each term in the sum is an excessive measure dominated by m. This result allows us to describe the Lebesgue decomposition of Q~ relative to Qm and t...

this is true for indicator functions, since ∫ 1Adπ = π(A) = ∫ A hπ,μdμ by definition of the Radon-Nikodym derivative. Then by linearity of the integral, the claim is also true for simple functions. Then we can show the claim for non-negative measurable functions, by approximating by simple functions. Indeed, if f ≥ 0 is measurable, then there exists a sequence of simple functions 0 ≤ sn ↑ f suc...

Let (G, τ ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If (G, τ ) has the A(iii)-property, then its completion (Ĝ, τ̂ ) is an order-complete locally solid lattice group. (2) If G is order-complete and τ has the Fatou property, then the order intervals of G are τ -complete. (3) If (G, τ ) has the Fatou property, then G is order-dense in Ĝ and...

The notions of compact convex variation and compact convex subdifferential for the mappings from a segment into a locally convex space (LCS) are studied. In the case of an arbitrary complete LCS, each indefinite Bochner integral has compact variation and each strongly absolutely continuous and compact subdifferentiable a.e. mapping is an indefinite Bochner integral. 0. Introduction and prelimin...

For any abelian Polish σ-compact group H there exist an Fσ ideal Z ⊆ P (N) and a Borel Z -approximate homomorphism f : H → HN which is not Z -approximable by a continuous true homomorphism g : H → HN .

and Applied Analysis 3 By 2.2 , we get μf,−q ( a pZp ) 2 q 2 qp −qa ∫ Zp f ( a px ) dμ−qpn x . 2.3 Therefore, by 2.3 , we obtain the following theorem. Theorem 2.1. For f, g ∈ C Zp , one has μαf βg,−q αμf,−q βμg,−q, 2.4 where α, β are constants. From 2.2 and 2.4 , we note that ∣μf,−q ( a pZp )∣∣ ≤ M‖f‖∞, 2.5 where ‖f‖∞ supx∈Zp |f x | and M is some positive constant. Now, we recall the definitio...

We establish a connection between the function space BMO and theory of quasisymmetric mappings on \emph{spaces homogeneous type} $\widetilde{X} :=(X,\rho,\mu)$. The is that logarithm generalised Jacobian an $\eta$-quasisymmetric mapping $f: \widetilde{X} \rightarrow \widetilde{X}$ always in $\rm{BMO}(\widetilde{X})$. In course proving this result, we first show $\widetilde{X}$, reverse-H\"{o}ld...

We discuss some known and some new results on the score function (SF) approach for simulation analysis. We show that while simulating a single sample path from the underlying system or from an associated system and applying the Radon-Nikodym measure one can: estimate the performance sensikGries (gradient, Hessian etc.) of the underlying system with respect to some parameter (vector of parameter...

We investigate variations on the problem to construct a measure with a given support. The variations include the available information about the set, whether the support has to be precisely the given set or merely a subset, and whether the measure is required to be non-atomic. A special case of particular importance is the Frostman lemma, which links having certain Hausdorff dimension to admitt...