The total variation of is defined by
It can be shown that, if is either or , every continuously differentiable (or piecewise continuously differentiable) function is of bounded variation (http://planetmath.org/ContinuousDerivativeImpliesBoundedVariation), and
If is also continuous, it is said to be a rectifiable path, and is the length of its trace.
If , it can be shown that is of bounded variation if and only if it is the difference of two monotonic functions.
|Date of creation||2013-03-22 13:26:09|
|Last modified on||2013-03-22 13:26:09|
|Last modified by||Koro (127)|