In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.
@article{urn:eudml:doc:41802, title = {A generalization of the Nikodym boundedness theorem.}, journal = {Collectanea Mathematica}, volume = {58}, year = {2007}, pages = {151-154}, zbl = {1129.28001}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41802} }
Stuart, Christopher. A generalization of the Nikodym boundedness theorem.. Collectanea Mathematica, Tome 58 (2007) pp. 151-154. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41802/