Let Be A Countably Infinite Set And Define En As The Smallest Class Of Subsets Of Such That For All Asa I If A Is Fini 1 (18.86 KiB) Viewed 80 times
sigma algebra
sigma algebra
Let Be A Countably Infinite Set And Define En As The Smallest Class Of Subsets Of Such That For All Asa I If A Is Fini 2 (18.86 KiB) Viewed 80 times
Let be a countably infinite set and define En as the smallest class of subsets of such that for all ASA (i) if A is finite, then A ein, and (ii) if A Efn, then Aº e in for AF:= (22 A). a) Show that the definition is non-trivial, i..., in general Bo 2 (Hint: find a set and a subset AC N which cannot be in in according to the above definition.) b) Would this change if In is defined as the largest class of subsets defined as above (instead of the smallest)? c) Prove or disprove that In is a c-algebra as defined in the lecture for any countably infinite set 22.
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