An exact Radon-Nikodym derivative is obtained for a pair (I,J) of positive linear functionals, with J absolutely continuous with respect to I, using a notion of exhaustion of I on elements of a function algebra lattice.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-1, author = {E. de Amo and M. D\'\i az Carrillo}, title = {A Radon-Nikodym derivative for positive linear functionals}, journal = {Studia Mathematica}, volume = {192}, year = {2009}, pages = {1-14}, zbl = {1184.28014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-1} }
E. de Amo; M. Díaz Carrillo. A Radon-Nikodym derivative for positive linear functionals. Studia Mathematica, Tome 192 (2009) pp. 1-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-1/