  The purpose of this note is to establish the following theorem: Let N be a
Kahler manifold, L be a compact oriented immersed minimal Lagrangian
submanifold in N and V be a holomorphic vector field in a neighbourhood of L in
N. Let div(V) be the (complex) divergence of V. Then the integral of div(V)
over L is 0. Vice versa let N^2n be Kahler-Einstein with non-zero scalar
curvature and L^n be a totally real oriented embedded n-dimensional
real-analytic submanifold of N s.t. the divergence of any holomorphic vector
field defined in a neighbourhood of L in N integrates to 0 on L. Then L is a
minimal Lagrangian submanifold of N.
