Let (G,M,μ) be a measure space, where μ is the Haar measure on topological group G:=R×R d , (R is the group of reals with the natural topology whereas R_d is the group of reals with the discrete topology) and M is the σ -algebra of all Haar measurable subsets of G .

Let μ_0 :=μ| B , where B is the σ -algebra of all Borel subsets in G , and let μ_0 to the smallest completion (G,M_1 ,μ 1 ) of the measure space (G,B,μ_o ) ?

Is it true that M_1 =M and consequently μ 1 =μ ?