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

Hôǹg Thái Nguyêñ, and Dariusz Pączka. "The Young Measure Representation for Weak Cluster Points of Sequences in M-spaces of Measurable Functions." Bulletin of the Polish Academy of Sciences. Mathematics 56.2 (2008): 109-120. <http://eudml.org/doc/281301>.

@article{HôǹgTháiNguyêñ2008,
abstract = {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 $ℝ^m$.},
author = {Hôǹg Thái Nguyêñ, Dariusz Pączka},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Young measure representation; weak cluster points of sequences in non--type spaces of measurable functions; -spaces; Banach lattices and non-solid generalized Orlicz spaces; Köthe–Bochner spaces},
language = {eng},
number = {2},
pages = {109-120},
title = {The Young Measure Representation for Weak Cluster Points of Sequences in M-spaces of Measurable Functions},
url = {http://eudml.org/doc/281301},
volume = {56},
year = {2008},
}

TY - JOUR
AU - Hôǹg Thái Nguyêñ
AU - Dariusz Pączka
TI - The Young Measure Representation for Weak Cluster Points of Sequences in M-spaces of Measurable Functions
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2008
VL - 56
IS - 2
SP - 109
EP - 120
AB - 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 $ℝ^m$.
LA - eng
KW - Young measure representation; weak cluster points of sequences in non--type spaces of measurable functions; -spaces; Banach lattices and non-solid generalized Orlicz spaces; Köthe–Bochner spaces
UR - http://eudml.org/doc/281301
ER -