A. Pelc, K. Prikry, On the existence of measures on sigma-algebras, Fundamenta Mathematicae 125 (1985), pp. 115-123.
We investigate the problem whether the existence of measures on a family of sub-algebras of an algebra A implies the existence of measures on A itself. Some relationships between various methods of constructing regularizing families for ultrafilters are also discussed in this context.
K. Ciesielski, A. Pelc, Extensions of invariant measures on Euclidean spaces, Fundamenta Mathematicae 125 (1985), pp. 1-10.
Sierpinski asked if there exists a maximal extension of the Lebesgue measure on the Euclidean space, invariant with respect to all isometries of this space. Our result implies a negative answer to this problem. We also show that for semiregular measures, the existence of proper invariant extensions depends on the size of continuum.