Consider F = {ER: either E is countable or Ec is countable}. (a) Show that F...

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Consider F = {ER: either E is countable or Ec is countable}. (a) Show that F is a o-algebra and F is a proper sub-o-algebra of the o-algebra BR. (b) Show that F is the o-algebra generated by {{x}: TER}. (c) Find a measure X: F→ [0, ∞] such that the only X-null set is Ø. Consider F = {ER: either E is countable or Ec is countable}. (a) Show that F is a o-algebra and F is a proper sub-o-algebra of the o-algebra BR. (b) Show that F is the o-algebra generated by {{x}: TER}. (c) Find a measure X: F→ [0, ∞] such that the only X-null set is Ø.

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