Prove that $BV[a,b]$ is the smallest linear space containing all monotone functions on $[a,b].$
2026-03-29 04:11:33.1774757493
Proving Bounded variation is smallest linear space
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Hint: You can use a result from the Jordan-Decomposition which states that $f$ is of bounded variation iff $f=f_1-f_2$ where $f_1,f_2$ are non decreasing functions.