2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115136In this paper we give some new criteria for identifying the components of a probability measure, in its Lebesgue decomposition. This enables us to give new criteria to identify spectral types of self-adjoint operators on Hilbert spaces, especially those of interest.10 pagesSymplectic Geometry47B15; 28A78text