Conclusions of transition mapping of the inverse limit space of X is proved as follow: (1) Strong nonewandering set of transition mapping equals the inverse limit space of strong nonewandering point set of mapping f. (2) f on the measure center is a nonwandering point set, if and only if the measure mapping of transition mapping is nonwandering point set on its measure center. f on the measure center is a strong nonwandering point set, only if the measure mapping of transition mapping is strong nonwandering point set on its measure center.