A. Pelc, K. Prikry, On the existence of measures on sigma-algebras,
*Fundamenta Mathematicae* 125 (1985), pp. 115-123.

Abstract:

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.

Abstract:

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.