Two-dimensional gauge fields with independent values of the field tensor at every point

Gauge invariant quantum measure is constructed for the some class of the two-dimensional Euclidean gauge fields in particular with the Lagrangian $\mathscr L_E=\frac1{4g^2}(F_{\lambda\mu},F_{\lambda\mu})$, the gauge group being an arbitrary compact Lie group. The measure is expressed in terms of the contour variables. The corresponding stress tensor $F_{\lambda\mu}(x)$ is a Gaussian generalised random field with independent values at each point. Some generalizations for the ease of non-Gaussian stress tensors are pointed out.