Editing Total variation (section)

{{Short description|Measure of local oscillation behavior}}
{{distinguish|Total variation distance of probability measures}}
{{primary sources|date=February 2012}}

In [[mathematics]], the '''total variation''' identifies several slightly different concepts, related to the ([[local property|local]] or global) structure of the [[codomain]] of a [[Function (mathematics)|function]] or a [[measure (mathematics)|measure]]. For a [[real number|real-valued]] [[continuous function]] ''f'', defined on an [[interval (mathematics)|interval]] [''a'', ''b''] ⊂ '''R''', its total variation on the interval of definition is a measure of the one-dimensional [[arclength]] of the curve with parametric equation ''x'' ↦ ''f''(''x''), for ''x'' ∈ [''a'', ''b'']. Functions whose total variation is finite are called ''[[Bounded variation|functions of bounded variation]]''.