The Young measure representation for weak cluster points of sequences in M-spaces of measurable functions

• Autorzy: Nguyen H. T. , Pączka D.
• Języki publikacji: EN

Abstrakty

EN

Let (X, Y) be a duality pair of M-spaces X, Y of measurable functions from Ω ⊂ R[sup]n into R[sup]d. The paper deals with Y-weak cluster points φ of the sequence φ(•, z[sub]j(•)) in X, where z[sub]j: Ω→ R[sup]m is measurable for j ∈ N and φ: Ω x R[sup]m → R[sup]d is a Carathéodory function. We obtain general sufficient conditions, under which, for some negligible set Aφ, the integral I(φ,νx) := ∫R φ(x,λ) dνx(λ) exists for χ ∈ Ω \ Aφ and φ(x) = I(φ, νx) on Ω \ Aφ, where ν = {νx}x∈Ω is a measurable-dependent family of Radon probability measures on R[sup]m.

Słowa kluczowe

EN

Young measure representation; weak cluster points of sequences in non-Lp-type spaces of measurable functions; M-spaces; Banach lattices and non-solid generalized Orlicz spaces; Köthe-Bochner space

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: Vol. 56, no 2
• Strony: 109--120
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Nguyen H. T.

autor

Pączka D.

• Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland,

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