  In this paper, we introduce new indices adapted to outputs valued in general
metric spaces. This new class of indices encompasses the classical ones; in
particular, the so-called Sobol indices and the Cram{\'e}r-von-Mises indices.
Furthermore, we provide asymptotically Gaussian estimators of these indices
based on U-statistics. Surprisingly, we prove the asymp-totic normality
straightforwardly. Finally, we illustrate this new procedure on a toy model and
on two real-data examples.
