Hi dear friends over the Internet, I have some questions on Papa Rudin: Question 1: On page 12 (proof of Theorem 1.9e), why is it that E is measurable? Question 2: On page the bottom of page 15 (the proof of Theorem 1.17), why are the φn's Borel functions? Also, the proposition states that f is a measurable function from X to [0,∞ ], but doesn't the definition (at least given in Def 1.3 on p8) require [0, ∞] being a topological space? Then what would be the topology of [0, ∞]? Thanks, any help is greatly appreciated.