  This paper deals with the possibility of transforming a weakly measurable
function in a Hilbert space into a continuous frame by a metric operator, i.e.,
a strictly positive self-adjoint operator. A necessary condition is that the
domain of the analysis operator associated to the function be dense. The study
is done also with the help of the generalized frame operator associated to a
weakly measurable function, which has better properties than the usual frame
operator. A special attention is given to lower semi-frames: indeed if the
domain of the analysis operator is dense, then a lower semi-frame can be
transformed into a Parseval frame with a (special) metric operator.
