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

• Autorzy: Hôǹg Thái Nguyêñ , Dariusz Pączka
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytski{\u\i}, Uryson, etc.)
• 46E40: Spaces of vector- and operator-valued functions
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46E27: Spaces of measures
• 28A33: Spaces of measures, convergence of measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: 56
• Numer: 2
• Strony: 109-120

Daty

wydano

2008

Twórcy

autor

Hôǹg Thái Nguyêñ

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

autor

Dariusz Pączka

• Institute of Mathematics, Szczecin University of Technology, Al. Piastów 48, 70-311 Szczecin, Poland

Identyfikatory

DOI

10.4064/ba56-2-3