Construction of a probability space.

  • #1
Q. Exhibit (if such exists) a probability space, denoted by (Ω, A, P[·]), which satisfies the following. For A1 and A2 members of A, if P[A1] = P[A2], then A1 = A2.

Answer: A = {Ω, ∅}, P[Ω] = 1 and P[∅] = 0. Is this a valid answer to the above question?
 

Answers and Replies

  • #2
haruspex
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Looks ok to me.
 
  • #3
Looks ok to me.

Thank you, haruspex!
 
  • #4
mathman
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If you want something more interesting, you can work with discrete sets. Example: 2 elements (A,B) with P(A) = 1/3 and P(B) = 2/3.
 
  • #5
If you want something more interesting, you can work with discrete sets. Example: 2 elements (A,B) with P(A) = 1/3 and P(B) = 2/3.

Thanks, mathman. I ended up doing something similar; constructed such a space for a biased coin.
 

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