  We study two geometrical factors needed for the correct construction of
statistical ensembles of surfaces. Such ensembles appear in the study of fluid
bilayer membranes, though our results are more generally applicable. The naive
functional measure over height fluctuations must be corrected by these factors
in order to give correct, self-consistent formulas for the free energy and
correlation functions of the height. While one of these corrections -- the
Faddeev-Popov determinant -- has been studied extensively, our derivation
proceeds from very simple geometrical ideas, which we hope removes some of its
mystery. The other factor is similar to the Liouville correction in string
theory. Since our formulas differ from those of previous authors, we include
some explicit calculations of the effective frame tension and two-point
function to show that our version indeed secures coordinate-invariance and
consistency to lowest nontrivial order in a temperature expansion.
