I am reading Kai Lai Chung's A Course in Probability Theory. In the proof of Theorem 9.3.4 on page 341 as shown below, where $\Lambda_j=\Lambda\bigcap\{\alpha=j\}$, I do not understand how the inequality below Inequality (17) is obtained, specifically how the integrating set $\{\beta\ge j\}$ disappears or is summed away. I would appreciate it if someone can explicate it.
