Analytic measures and Bochner measurability
| dc.creator | Asmar, N. | |
| dc.creator | Montgomery-Smith, Stephen J. | |
| dc.date | 1995-01-10 | |
| dc.date | 1999-12-06 | |
| dc.date.accessioned | 2026-07-07T09:04:43Z | |
| dc.date.available | 2026-07-07T09:04:43Z | |
| dc.description | Let $Σ$ be a $σ$-algebra over $Ω$, and let $M(Σ)$ denote the Banach space of complex measures. Consider a representation $T_t$ for $t\in\Bbb R$ acting on $M(Σ)$. We show that under certain, very weak hypotheses, that if for a given $μ\in M(Σ)$ and all $A \in Σ$ the map $t \mapsto T_t μ(A)$ is in $H^\infty(\Bbb R)$, then it follows that the map $t \mapsto T_t μ$ is Bochner measurable. The proof is based upon the idea of the Analytic Radon Nikodým Property. Straightforward applications yield a new and simpler proof of Forelli's main result concerning analytic measures ({\it Analytic and quasi-invariant measures}, Acta Math., {\bf 118} (1967), 33--59). | |
| dc.identifier | https://arxiv.org/abs/math/9501211 | |
| dc.identifier | http://arxiv.org/abs/math/9501211 | |
| dc.identifier | Bull. Sc. Math. 122, (1998), 39-66 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149479 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46G10 | |
| dc.title | Analytic measures and Bochner measurability | |
| dc.type | text |