Robustness of statistical manifolds

Topology consisting of statistical structures induced by ( Gromov implicit function theorem, we show robustness of the generic statistical structure induced on M by the standard linear statistical structure on RN , for N sufficiently large. A statistical structure (g, T) on a smooth manifold M induced by ( said to be robust if there exists an open neighborhood of (g, T) in the fine C infinity- T tilde ). Using Nash- tilde M, g tilde , T tilde ) is tilde M, g tilde ,(c) 2023 Elsevier B.V. All rights reserved.