Sentence:  <WSD>Monotone functions</WSD> on [a, b] have nice properties. For example, they are integrable on [a, b] and have only a countable number of jump discontinuities. In this section, we shall also show that every <WSD>monotone function</WSD> is a function of bounded variation, and hence the class \mathit{BV}([a,b]) contains the class of <WSD>monotone functions</WSD> on [a, b]. 
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").