Geodesic
Linear Isometries of Spaces of Absolutely Continuous Functions
Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 298-306

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be an arbitrary compact subset of the real line R which has at least two points. For each finite complex valued function f on X we denote by V(f; X) (and call it the weak variation of f on X) the least upper bound of the numbers ∑i|f(bi ) – f(ai )| where {[ai , bi ]} is any sequence of non-overlapping intervals whose end points belong to X. A function f is said to be of bounded variation (BV) on X if V(f; X) < ∞. A function f is said to be absolutely continuous (AC) on X, if given any ∈ > 0 there exists an n > 0 such that for every sequence of non-overlapping intervals {[au bi]} whose end points belong to X, the inequality implies that ([7], p. 221, 223). 
Pathak, V. D. Linear Isometries of Spaces of Absolutely Continuous Functions. Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 298-306. doi: 10.4153/CJM-1982-019-7
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