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We prove an analogue of the Lebesgue decomposition for continuous functionalson the commutant modulo a reflexive normed ideal of an n-tuple of hermitianoperators for which there are quasicentral approximate units relative to thenormed ideal. Using results of Godefroy-Talagrand and Pfitzner we derive fromthis strong uniqueness of the predual of such a commutant modulo a normedideal.

Lebesgue decomposition of functionals and unique preduals for commutants modulo normed ideals