Exercise 14, § 3

Let $(T_i)_{i \in I}$ be a family of Radon topological spaces, and $T$ the sum space of the family. If Card(I) is an Ulam cardinal, then the topological space $T$ is a Radon space (show that for every positive and bounded countably additive function $m$ on the Borel tribe of $T$, there exists a countable subset $J$ of $I$ such that $m(\bigcup_{i \in I - J} T_i) = 0$).