  We construct a Gibbs measure for the nonlinear Schrodinger equation (NLS) on
the circle, conditioned on prescribed mass and momentum: d \mu_{a,b} = Z^{-1}
1_{\int_T |u|^2 = a} 1_{i \int_T u \bar{u}_x = b} exp (\pm1/p \int_T |u|^p -
1/2 \int_{\T} |u|^2) d P for a \in R^+ and b \in R, where P is the
complex-valued Wiener measure on the circle. We also show that \mu_{a,b} is
invariant under the flow of NLS. We note that i \int_\T u \bar{u}_x is the Levy
stochastic area, and in particular that this is invariant under the flow of
NLS.
