具有Smital性质的理想
Ideals with Smital properties
摘要：
波兰群$(X,+)$上的$σ$ -理想$\mathcal{I}$具有Smital性质，如果对每个稠密集$D$和Borel $\mathcal{I}$ -正集$B$，其代数和$D+B$是来自$\mathcal{I}$的集合的补.我们考虑这个属性的几个变体，并研究它们与可数链条件，极大性的联系，以及它们如何通过Fubini产品保存。
英文摘要：
A $σ$-ideal $\mathcal{I}$ on a Polish group $(X,+)$ has Smital Property if for every dense set $D$ and a Borel $\mathcal{I}$-positive set $B$ the algebraic sum $D+B$ is a complement of a set from $\mathcal{I}$. We consider several variants of this property and study their connections with countable chain condition, maximality and how well they are preserved via Fubini products.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
