  Regge calculus is considered as a particular case of the more general system
where the linklengths of any two neighbouring 4-tetrahedra do not necessarily
coincide on their common face. This system is treated as that one described by
metric discontinuous on the faces. In the superspace of all discontinuous
metrics the Regge calculus metrics form some hypersurface. Quantum theory of
the discontinuous metric system is assumed to be fixed somehow in the form of
quantum measure on (the space of functionals on) the superspace. The problem of
reducing this measure to the Regge hypersurface is addressed. The quantum Regge
calculus measure is defined from a discontinuous metric measure by inserting
the $\delta$-function-like phase factor. The requirement that this reduction
would respect natural physical properties (positivity, well-defined continuum
limit, absence of lattice artefacts) put rather severe restrictions and allows
to define practically uniquely this phase factor.

General Relativity and Quantum Cosmology