EDA search space

Question

I am supposed to demonstrate that the Estimation of Distribution Algorithm's (EDA) search space shrinks exponentially fast if learning in iteration t produces

P'(X) = P^(G(t)) (X)

with

G(t) = arg max {F(x)}

Regardless of the problem or type of x.

P = population
n = population size = infinite

Could you give me some starting points? I've spent the entire day searching on Google for information but couldn't find something to really help me.