Uniqueness of the gauge-invariant Fujikawa measure for the bosonic string

In this paper, the authors fix the gauges of the bosonic string by eμa- hμa = 0 with hμa a general background vielbein, choose bar X = Xhk, bar C = Chm and bar C* = C*hn as independent path-integral variables where (C*)C are the propagating parts of the coordinate (anti)ghosts and h = det hμa, and regulate the measure by general (k, m, n-dependent) consistent regulators. Background gauge independence of the measure then uniquely fixes k, m, n to the values proposed by Fujikawa. Ambiguities in the measure reported in the literature are due to using the conformal gauge and are fixed in a general background gauge