The paper considers a nonlinear functional Rayleigh-Ritz operator defined on a set of pairs of measurable functions. It is equal to the ratio of their moduli, when the denominator is nonzero, and to zero in the opposite case. Continuity of this operator with respect to convergence and also with respect to the measure is investigated. It has been demonstrated that convergence of the operator’s value on the sequence of pairs to the value on the limit pair of functions necessitates not only convergence with respect to the measure of its arguments but also convergence with respect to the measure of carriers of the second argument to the carrier of its limit. The results obtained may be applied in the theory of differential realization (in the Hilbert space) of nonlinear dynamic models of higher orders.

space of measurable functions, convergence with respect to the measure, noninvariant metric, Rayleigh-Ritz operator.