Construction of Invariant Non-separable Extensions of the Measure Defined by H-valued Measurable G-process on H

For an arbitrary infinite additive group G and for an uncountable compact Hausdorff topological group H with card(H) = card(Hא0) = card(H), H-valued measurable Gprocesses are constructed on the group H and some set-theoretical characteristics of their various F∗(HG)-invariant extensions are calculated, where F∗(HG) denotes a group of transformations of H generated by the eventually neutral sequences and all permutations of G. More precisely, an orthogonal family of F∗(HG)-invariant extensions of the left-invariant probability Haar-Baire measure on H is constructed such that topological weights of metric spaces associated with such extensions are maximal. In addition, for such a family of measures in H, the F∗(HG)-invariant measure extension problem is studied.