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Bounded Variation

  • Definition: A function f(x) is said to have bounded variation if, over the closed interval x in [a,b], there exists an M such that |f(x_1)-f(a)|+|f(x_2)-f(x_1)|+ ... +|f(b)-f(x_(n-1))|<= M for all a < x_1 < x_2 < ... < x_(n-1) < b.


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