Construction of a probability space.

[chocolatefrog]

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?

 

[haruspex]

Looks ok to me.

 

[chocolatefrog]

Looks ok to me.

Thank you, haruspex!

 

[mathman]

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.

 

[chocolatefrog]

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.