Find the Total Variation of a Function

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.

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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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