Let (X,A, μ) be a complete probability space,\rho a lifting, and T_\rhothe associated Hausdorff lifting topology on X.Suppose F : (X, T\rho) → E′′_\sigma be a bounded continuous mapping. It isproved that there is an A ∈ A such that F_{\chi A}has range in a closedseparable subspace of E (so F_{\chi A} : X → Eis strongly measurable)and for any B ∈ A with μ(B) > 0 andB ∩ A = \emptyset, F_{\chi,B} cannotbe weakly equivalent to a E-valued strongly measurable function.Some known results are obtained as corollaries.
@article{124,
title = {A DECOMPOSITION OF BOUNDED, WEAKLY MEASURABLE FUNCTIONS},
journal = {Tatra Mountains Mathematical Publications},
volume = {49},
year = {2011},
doi = {10.2478/tatra.v49i0.124},
language = {EN},
url = {http://dml.mathdoc.fr/item/124}
}
Khurana, Surjit Singh. A DECOMPOSITION OF BOUNDED, WEAKLY MEASURABLE FUNCTIONS. Tatra Mountains Mathematical Publications, Tome 49 (2011) . doi : 10.2478/tatra.v49i0.124. http://gdmltest.u-ga.fr/item/124/