Editing Total variation (section)

===Total variation for functions of one real variable===
{{EquationRef|1|Definition 1.1.}} The '''total variation''' of a [[real number|real]]-valued (or more generally [[complex number|complex]]-valued) [[function (mathematics)|function]] <math>f</math>, defined on an [[interval (mathematics)|interval]] <math> [a , b] \subset \mathbb{R}</math> is the quantity

:<math> V_a^b(f)=\sup_{\mathcal{P}} \sum_{i=0}^{n_P-1} | f(x_{i+1})-f(x_i) |, </math>

where the [[supremum]] runs over the [[Set (mathematics)|set]] of all [[partition of an interval|partitions]] <math> \mathcal{P} = \left\{P=\{ x_0, \dots , x_{n_P}\} \mid P\text{ is a partition of } [a,b] \right\} </math> of the given [[interval (mathematics)|interval]]. Which means that <math>a = x_{0} < x_{1} <  ...  < x_{n_{P}} = b</math>.