Manifolds of continuous functions of bounded variation and vector measure regularity of Banach-Lie groups

We construct a smooth Banach manifold BV(a,b,M) whose elements are suitably-defined functions f : a,b -> M of bounded variation with values in a smooth Banach manifold M which admits a local addition. If the target manifold is a Banach-Lie group G, with Lie algebra g, we obtain a Banach-Lie group BV(a,b,G) with Lie algebra BV(a,b,g). Strengthening known regularity properties of Banach-Lie groups, we construct a smooth evolution map from a Banach space of g-valued vector measures on 0,1 to BV(0,1,G).