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Needs:
Sigma Algebras ›
Monotone Classes ›
Needed by:
None.
Links:
Sheet PDF ›
Graph PDF ›

Monotone Algebras

Why

Closure under monotone limits is a weaker condition than that included in the definition of sigma algebras, but is sufficient if the set is also an algebra.1

Result

If a subset algebra is a monotone space, then it is a countably summable subset algebra.

A subset algebra is a countably summable if either:
  1. the limit of a nondecreasing sequence of distinguished sets is distinguished
  2. the limit of a nonincreasing sequence of distinguished sets is distinguished.
  1. Future editions will expand. ↩︎
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