Appendix A Definition of Gâteaux and Fréchet derivatives

Whence we get the simpler assumption (A" In other cases, one needs more specific theorems such as Dunford-Pettis' theorem for L The other conditions are difficult to verify for given functionals. We conclude by using Lemma 13. In this space, the shortest distance paths between measures are given by their square-norm distance. While both frameworks yield optimisation algorithms on measure spaces, the geometries and algorithms are very different. F is decreasing at each iteration.