Assignment:
In this exercise we show that Theorem does not hold without the assumption that P(ω) > 0 for every state of the world ω ∈ Y . Prove that there exists an Aumann model of incomplete information in which the common prior P satisfies P(ω) = 0 in at least one state of the world ω ∈ Y , such that the following claim holds: the knowledge operator in the Aumann model is not identical to the belief operator in the belief space ? equivalent to the Aumann model.
Provide complete and step by step solution for the question and show calculations and use formulas.