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High Quality Content by WIKIPEDIA articles! In mathematics, the total variation of a real-valued function , defined on an interval [a, b] R is a measure of the one-dimensional arclength of the curve with parametric equation x (x), for x [a,b]. The total variation is a norm defined on the space of measures of bounded variation. The space of measures on a -algebra of sets is a Banach space, called the ca space, relative to this norm. It is contained in the larger Banach space, called the ba space, consisting of finitely additive (as opposed to countably additive) measures, also with the same norm.