Definition:Limit of Decreasing Sequence of Sets

Definition

Let $\sequence {S_n}_{n \mathop \in \N}$ be a decreasing sequence of sets.

Let $S = \ds \bigcap_{n \mathop \in \N} S_n$.

Then $S$ is said to be the limit of $\sequence {S_n}_{n \mathop \in \N}$, and one writes $S_n \downarrow S$.

Also see

• Limit of Increasing Sequence of Sets
• Decreasing Sequence of Sets

Sources

• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 4$