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An Application of Independent Families of Sets to the Measure Extension Problem

Abstract The method of independent families of sets elaborated by Tarski [Set theory. With an introduction to descriptiveset theory, PWN–Polish Scientific Publishers, 1976] and Kakutani and Oxtoby [Ann. of Math. 52: 580–590, 1950] is applied to the construction of maximal (in the sense of cardinality) families of pairwise orthogonal nonseparable invariant extensions of Haar measures.