# Find the Total Variation of a Function

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The total variation of a function over the interval is the supremum (or least upper bound) of taken over all partitions of the interval . The total variation is a measure of the oscillation of the function over the interval . If is finite, then is of bounded variation on the interval.

Contributed by: Izidor Hafner (December 2015)

Open content licensed under CC BY-NC-SA

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Reference

[1] E. J. Borowski and J. M. Borwein, *Collins Dictionary of Mathematics*, New York: HarperCollins Publishers, 1989.

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"Find the Total Variation of a Function"

http://demonstrations.wolfram.com/FindTheTotalVariationOfAFunction/

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Published: December 30 2015