2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119114An arbitrary linear relation (multivalued operator) acting from one Hilbert space to another Hilbert space is shown to be the sum of a closable operator and a singular relation whose closure is the Cartesian product of closed subspaces. This decomposition can be seen as an analog of the Lebesgue decomposition of a measure into a regular part and a singular part. The two parts of a relation are characterized metrically and in terms of Stone's characteristic projection onto the closure of the linear relation.to appear in Acta Math. Hungarica, volume 116(1-2)Functional AnalysisMathematical Physics47A05, 47A06text