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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2603.19392 |
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Table des matières:
- It is shown that for any finite positive measure $μ$ defined on a measure space $(S, Σ)$, and any Banach or Fréchet space $Z$, the control measure Theorem of Talagrand (T) is true for the case when the (stochastic) vector measure $\boldsymbol{m}:\mathcal{E} \to L_0(μ,Z)$, defined on another measurable space $(E, \mathcal{E})$, takes values in $L_{0}(μ,Z)$, the Bochner space of vector-valued functions associated to $μ$ and $Z$. As a consequence, we also obtain a Rybakov type result for this control. Finally, we give the relation of this result to bounded multiplier properties (BMP) of $F$-spaces and pose various open problems related to it.