Who knowsIf 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!

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Who knowsIf 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!

Jaida Sanders · Accepted Answer

You&#039;re intersecting algebras (that contain   A) not subsets. Mind your types..

Who knows If I define algebra <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphi

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