Definition:Limit of Increasing Sequence of Sets
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Definition
Let $\sequence {S_n}_{n \mathop \in \N}$ be an increasing sequence of sets.
Let $S = \ds \bigcup_{n \mathop \in \N} S_n$.
Then $S$ is said to be the limit of $\sequence {S_n}_{n \mathop \in \N}$, and one writes $S_n \uparrow S$.
Also see
Sources
- 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 4$