Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140122244
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