  Euler integrals of deterministic functions have recently been shown to have a
wide variety of possible applications, including in signal processing, data
aggregation and network sensing. Adding random noise to these scenarios, as is
natural in the majority of applications, leads to a need for statistical
analysis, the first step of which requires asymptotic distribution results for
estimators. The first such result is provided in this paper, as a central limit
theorem for the Euler integral of pure, Gaussian, noise fields.
