  This paper presents a general formalism that allows the derivation of the
cumulant generating function and one-point Probability Distribution Function
(PDF) of the aperture mass ($\hat{M}_{ap}$), a common observable for cosmic
shear observations. Our formalism is based on the Large Deviation Principle
(LDP) applied, in such cosmological context, to an arbitrary set of densities
in concentric cells. We show here that the LDP can indeed be used for a much
larger family of observables than previously envisioned, such as those built
from continuous and nonlinear functionals of the density profiles. The general
expression of the observable aperture mass depends on reduced shear profile
making it a rather involved function of the projected density field. Because of
this difficulty, an approximation that is commonly employed consists in
replacing the reduced shear by the shear in such a construction neglecting
therefore non-linear effects. We were precisely able to quantify how this
approximation affects the $\hat{M}_{ap}$ statistical properties. In particular
we derive the corrective term for the skewness of the $\hat{M}_{ap}$ and
reconstruct its one-point PDF.
