A decomposition of bounded, weakly measurable functions

Rok, strany: 2011, 67 - 70

Let $(X, \mathcal{A}, μ)$ be a complete probability space, $ρ$ a lifting, $\mathcal{T}_ρ$ the associated Hausdorff lifting topology on $X$ and $E$ a Banach space. Suppose $F\colon (X, \mathcal{T}_ρ) \to E''_σ $ be a bounded continuous mapping. It is proved that there is an $A \in \mathcal{A}$ such that $F χ_A$ has range in a closed separable subspace of $E$ (so $F χ_A\colon X \to E$ is strongly measurable) and for any $ B \in \mathcal{A}$ with $ μ(B) >0$ and $B \cap A = \emptyset$, $F χ_B$ cannot be weakly equivalent to a $E$-valued strongly measurable function. Some known results are obtained as corollaries.

ISO 690:

Khurana, S. 2011. A decomposition of bounded, weakly measurable functions. In Tatra Mountains Mathematical Publications, vol. 49, no.2, pp. 67-70. 1210-3195.

APA:

Khurana, S. (2011). A decomposition of bounded, weakly measurable functions. Tatra Mountains Mathematical Publications, 49(2), 67-70. 1210-3195.