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Construction of a probability space.

  1. Aug 25, 2012 #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?
  2. jcsd
  3. Aug 25, 2012 #2


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    Looks ok to me.
  4. Aug 26, 2012 #3
    Thank you, haruspex!
  5. Aug 26, 2012 #4


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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.
  6. Aug 29, 2012 #5
    Thanks, mathman. I ended up doing something similar; constructed such a space for a biased coin.
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