Sentence:  Section 1 contains Lebesgue's main tool, a theorem saying that <WSD>monotone functions</WSD> on the line are differentiable almost everywhere. 
Meaning of the word marked with <WSD> tags:  A function "f" : "X"→'''R''' (where "X" is a subset of '''R''', possibly a discrete set) that either never decreases or never increases as its independent variable increases; that is, either "x" ≤ "y" implies "f"("x") ≤ "f"("y") or "x" ≤ "y" implies "f"("y") ≤ "f"("x").