  Colombeau's generalized functions are used to adapt the distributional
approach to singular hypersurfaces in general relativity with signature change.
Equations governing the dynamics of singular hypersurface is obtained and it is
shown that matching leads to de Sitter space for the Lorentzian region. The
matching is possible for different sections of the de Sitter hyperboloid. A
relation between the radius of $S^4$, as the Euclidean manifold, and the
cosmological constant leading to inflation after signature change is obtained.
