Non-isomorphism of A∗n,2≤n≤∞, for a non-separable abelian von Neumann algebra A

We prove that if A is a non-separable abelian tracial von Neuman algebra then its free powers A ∗ n ,2≤ n ≤∞, are mutually non-isomorphic and with trivial fundamental group, F(A*n)=1 , whenever 2≤ n <∞. This settles the non-separable version of the free group factor problem.