A statistical structure $(g, T)$ on a smooth manifold $M$ induced by $(\tilde M, \tilde g, \tilde T)$ is said to be {\em robust} if there exists an open neighborhood of $(g,T)$ in the fine $C^{\infty}$-topology consisting of statistical structures induced by $(\tilde M, \tilde g, \tilde T)$. Using Nash--Gromov implicit function theorem, we show robustness of the generic statistical structure induced on $M$ by the standard linear statistical structure on ${\R}^N$, for $N$ sufficiently large.

翻译：由$(\ tilde M, \ tilde g, \ tilde T) 诱导的平滑元体美元统计结构$(g, T) $(m) 的统计结构据说是 $(t) 坚固 } 如果在由$(\ tilde M, \ tilde g, \ tilde T) 诱导的统计结构中存在一个开放区$(g, T) $(g, T), 由$( tilde g, \ tilde T) 构成。 使用 Nash- Gromov 隐含的理论功能, 我们以足够大的$( $ ) 的标准线性统计结构所引致的通用统计结构的坚固性, 则由$( R) $( n) 相当大的美元 。