In the entire functions space [ 2, πq 2s2 ) consisting of at most second order functions such that their type is less than πq/(2s) it is valid the qorder derivative sampling series reconstruction procedure, reading at the von Neumann lattice {s(m + ni)| (m,n) ∈ Z2} via the Weierstrass σ(·) as the sampling function, s > 0. The uniform convergence of the sampling sums to the initial function is p...

We define an integral of real-valued functions with respect to a measure that takes its values in the extended positive cone partially ordered vector space $E$. The monotone convergence theorem, Fatou's lemma, and dominated theorem are established; analogues classical ${\mathcal L}^1$- ${\mathrm L}^1$-spaces investigated. results extend earlier work by Wright specialise those for Lebesgue when ...

Abstract The main purpose of this paper is to apply the theory vector lattices and related abstract modular convergence context Mellin-type kernels (non)linear lattice-valued operators, following construction an integral given in earlier papers.

A convergence in Riesz spaces is given axiomatically. A Bochner-type integral for Riesz space-valued functions is introduced and some Vitali and Lebesgue dominated convergence theorems are proved. Some properties and examples are investigated. A.M.S. SUBJECT CLASSIFICATION (2000): 28B15.

The concept of ${mathscr{F}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{F}}$. Its equivalence to the concept of ${mathscr{F}}$-convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.

The main purpose of this paper is to investigate constructively the relationship between proximal convergence, uniform sequential convergence and uniform convergence for sequences of mappings between apartness spaces. It is also shown that if the second space satisfies the Efremovic axiom, then proximal convergence preserves strong continuity. Mathematics Subject Classification: 54E05, 03F60

A net (xγ)γ∈Γ in a locally solid Riesz space (X,τ) is said to be unbounded τ-convergent x if |xγ−x|∧u⟶τ0 for all u∈X+. We recall that there linear topology uτ on X such τ-convergence coincides with uτ-convergence. It turns out characterised as the weakest which τ order bounded subsets. this motivation we introduce, uniform lattice (L,u), uniformity u⁎ L u subsets of L. shown induced by (X,τ), t...

Our starting point is the Mosco-convergence result due to Hess ((He'89]) for integrable multivalued supermartingales whose values may be unbounded, but are majorized by a w-ball-compact-valued function. It is shown that the convergence takes place also in the slice topology. In the case when both the underlying space X and its dual X have the Radon-Nikodym property a weaker compactness assumpti...