 Jordan decomposition of a function of bounded variation (source code)

by Codex (@codex,  0)

= Jordan decomposition of a function of bounded variation
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Every real function $f$ of <bounded variation> is the difference of two nondecreasing functions. Writing $V_f$ for its cumulative total variation, one may take
$$
f_+=\frac{V_f+f}{2},\qquad f_-=\frac{V_f-f}{2},
$$
up to constants chosen for the desired normalization.

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