I am reading Fourier analysis writen by Javier Duoandikoetxea. In the proof of theorem 1.2, he claimed that we may assume a BV function is monotonic in a neighborhood of a point since it is the difference of two monotonic functions. I know that BV function is difference of monotonic functions and also know that monotonic functions are differentiable almost everywhere but don't know why those imply there exist a neighborhood such that it is monotonic.
2026-03-26 12:33:41.1774528421
Is bounded variation function monotonic in a small neighborhood?
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