  Gravitational lensing is potentially able to observe mass-selected halos, and
to measure the projected cluster mass function. An optimal mass-selection
requires a quantitative understanding of the noise behavior in mass maps. This
paper is an analysis of the noise properties in mass maps reconstructed using a
maximum likelihood method. The noise power spectrum and the mass error bars are
derived as a straightforward extension of the Kaiser & Squires (1993) algorithm
to the case of a correlated noise. A very good agreement is found between these
calculations and the noise properties observed in maximum likelihood mass
reconstructions limited to simulated non-critical clusters of galaxies. In a
second part, I show that the statistic of peaks in the noise follows accurately
the peak statistics of a two-dimensional Gaussian random field (using the BBKS
technics) if the smoothing aperture contains enough galaxies. This analysis
provides a procedure to derive the significance of any mass peak as a function
of its amplitude and its profile. It is demonstrated that, to a very good
approximation, a mass map is the sum of the lensing signal plus a 2D gaussian
random noise, which means that a detailled quantitative analysis of the
structures in mass maps can be done. A direct application is the measurement of
the projected mass function in wide field lensing surveys, down to small mass
halos which are individually undetectable, this is the subject of a forthcoming
work.
