Assignment:
Let (N, Y, (Fi)i∈N, s, P) be an Aumann model of incomplete information with beliefs, and let W ⊆ Y be an event. Prove that (N,W, (Fi ∩ W)i∈N , P(· | W)) is also an Aumann model of incomplete information with beliefs, where for each player i ∈ N Fi ∩ W = {F ∩ W : F ∈ Fi} is the partition Fi restricted to W, and P(· | W) is the conditional distribution of P over W.
Provide complete and step by step solution for the question and show calculations and use formulas.