Exercise 8, § 4

With the notations of Exercise 6, show that if the product of the family $(\mu_\lambda)$ is defined and $\neq 0$, then there exists a countable subset $K$ of $L$ such that for every $\lambda \in L - K$, the measure $\mu_\lambda$ is positive and of total mass 1 (make use of Exer. 18 of §1).