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Total Variation

  • Definition: Let f be of bounded variation [a, b], and let sum(P) denote the sum sum(|delta f_k|), as k goes from 1 to n, corresponding to the partition P of [a, b]. The number V_f(a, b) = sup{sum(P) such that P is a partition of [a, b]} is called the total variation of f on the interval [a, b].

    Source: Mathematical Analysis, second edition by Tom M. Apostol

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