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  "body": "\n## Summary\n\nThe total variation of a real function on an interval measures how much its values change in total, counting each rise and each fall.\nIt is the supremum of the sums of the absolute changes over all partitions of the interval.\nA function has [[bounded variation|A8251BHCMP]] exactly when its total variation is finite.\nThe same idea gives the total variation of a signed measure and of functions of several variables.\n\n## Explanations\n\n### L1 human\n\nThink of the graph of a function as a mountain path and measure only the height you climb plus the height you descend.\nThe total variation is this sum of heights.\nFor $f(x) = \\sin x$ on $[0, 2\\pi]$ you go up by $1$, down by $2$, and up by $1$, so the total variation is $4$.\nFor a monotone function the total variation is just the difference between the end values.\n",
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