Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.

还进一步建立了当扰动趋于零时，关于这族不变测度的大偏差原理。

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By traditional method of large deviations, we obtain the logarithmic asymptotic for the probabilities and large deviation principle for the corresponding measures.

利用经典大偏差的方法，在一定的条件下，得到了相应概率的对数渐近式及测度族的大偏差原理。

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