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The Young Measure Representation for Weak Cluster Points of Sequences in M-spaces of Measurable Functions

Hôǹg Thái Nguyêñ, Dariusz Pączka (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

Let ⟨X,Y⟩ be a duality pair of M-spaces X,Y of measurable functions from Ω ⊂ ℝ ⁿ into d . The paper deals with Y-weak cluster points ϕ̅ of the sequence ϕ ( · , z j ( · ) ) in X, where z j : Ω m is measurable for j ∈ ℕ and ϕ : Ω × m d is a Carathéodory function. We obtain general sufficient conditions, under which, for some negligible set A ϕ , the integral I ( ϕ , ν x ) : = m ϕ ( x , λ ) d ν x ( λ ) exists for x Ω A ϕ and ϕ ̅ ( x ) = I ( ϕ , ν x ) on Ω A ϕ , where ν = ν x x Ω is a measurable-dependent family of Radon probability measures on m .

The ν ( ρ ) -transformation on McBride’s spaces of generalized functions

Domingo Israel Cruz-Báez, Josemar Rodríguez (1998)

Commentationes Mathematicae Universitatis Carolinae

An integral transform denoted by ν ( ρ ) that generalizes the well-known Laplace and Meijer transformations, is studied in this paper on certain spaces of generalized functions introduced by A.C. McBride by employing the adjoint method.

The σ -property in C ( X )

Anthony W. Hager (2016)

Commentationes Mathematicae Universitatis Carolinae

The σ -property of a Riesz space (real vector lattice) B is: For each sequence { b n } of positive elements of B , there is a sequence { λ n } of positive reals, and b B , with λ n b n b for each n . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “ σ ” obtains for a Riesz space of continuous real-valued functions C ( X ) . A basic result is: For discrete X , C ( X ) has σ iff the cardinal | X | < 𝔟 , Rothberger’s bounding number. Consequences and...

Théorème du graphe fermé dans les G-espaces topologiques.

R. Ameziane Hassani, A. Blali, A. Bouziani (2004)

Extracta Mathematicae

In this paper we introduce the notion of topological G-spaces. This is an intermediate class between G-sets and A-modules. After giving suitable definitions and illustrating examples, we prove a theorem of closed graph theorem type.

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