Wyniki wyszukiwania - BazTech

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 2008

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: M-spaces

Sortuj według:

Ogranicz wyniki do:

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

Nguyen H. T., Pączka D.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

Vol. 56, no 2

109-120

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.