Who knowsIf I define algebra F ( A ) generated by A, collection of subsets...

Villaretq0

Villaretq0

Answered

2022-06-14

Who knows
If I define algebra F ( A ) generated by A, collection of subsets of S (the universal set) as the intersection of F , algebra superset of A:
F ( A ) = a l g e b r a   F A F
What if A is an infinite (either countable or uncountable) set? Algebra, unlike σ-algebra, guarantees being closed under finite Boolean operations. Here, finite(in the definition of algebra) and infinite(in the setting) confuses me. e.g. A is the collection of intervals ( , x ]( x R ) and S = R , what F ( A ) be like? Any help will be appreciated!

Answer & Explanation

Jaida Sanders

Jaida Sanders

Expert

2022-06-15Added 18 answers

You're intersecting algebras (that contain A) not subsets. Mind your types..

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