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Bounded Variation

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

\begin{displaymath}
\vert f(x_i)-f(a)\vert+\vert f(x_2)-f(x_1)\vert+\ldots +\vert f(b)-f(x_{n-1})\vert \leq M
\end{displaymath}

for all $a < x_1 < x_2 < \ldots < x_{n-1} < b$.




© 1996-9 Eric W. Weisstein
1999-05-26