Stability theorem for the Feynman integral via time continuation

Lapidus proved a stability theorem for the Feynman integral as a bounded li near operator on L-2(R-d) with respect to potential functions. We establish a stability theorem for the Feynman integral with respect to measures whos e positive and negative variations are in the generalized Kato class. This is a partial extension of Lapidus's result. In fact, we develop our stabili ty theorem under a more general setting in the sense that potential functio ns in Lapidus's paper are involved in the Kato class and the measures in th is paper are involved in the generalized Kato class which generalizes subst antially the Kato class.