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Can the $L^1$ - $L^\infty$ duality be restored for non-dominated families of probability measures?Can the $L^1$-$L^\infty$ duality be restored for non-dominated families of probability measures?

Irene Klein · Georg Köstenberger首次提交 2026-05-06 · 修订 2026-05-13 · v2arXiv预印本

非受控概率测度族下能否恢复 L¹–L∞ 对偶性？AI 解读

The duality $L^{\infty}\simeq (L^{1})'$ frequently breaks down in the presence of model uncertainty, where a single reference measure $P$ is replaced by a non-dominated family of probability measures $\mathcal{P}$ . The unavailability of classical measure-theoretic and functional-analytic tools in this regime poses a significant obstacle to developing robust probabilistic frameworks. We show that this duality can be restored for a broad class of robust statistical models by…The duality $L^{\infty}\simeq (L^{1})'$ frequently breaks down in the presence of model uncertainty, where a single reference measure $P$ is replaced by a non-dominated family of probability measures $\mathcal{P}$. The unavailability of classical measure-theoretic and functional-analytic tools in this regime poses a significant obstacle to developing robust probabilistic frameworks. We show that this duality can be restored for a broad class of robust statistical models by…

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关联记录被引 0 次 ↗OpenAlex · 核验 2026-10-01

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Can the L1L^1L1-L∞L^\inftyL∞ duality be restored for non-dominated families of probability measures?Can the $L^1$-$L^\infty$ duality be restored for non-dominated families of probability measures?

Can the $L^1$ - $L^\infty$ duality be restored for non-dominated families of probability measures?Can the $L^1$-$L^\infty$ duality be restored for non-dominated families of probability measures?