We use an electrical impedance technique to measure the fluctuations of gas volume fraction in a gas-liquid bubble column in turbulent flow regime. From these experimental values the volume fraction autocorrelation function is determined. On the theoretical side, we introduce a stochastic model to describe the aggregation of bubbles by assuming them to be rigid spheres of different diameters and by considering their coalescence as a stochastic Markovian process. The coalescence rate contains one adjustable parameter which takes into account the neglected effects of compressibility and deformation, spatial inhomogeneities and hydrodynamic interactions between the bubbles and with the boundaries. The associated master equation for this polydispersed system is built up, and from it we derive an equation for the volume fraction equilibrium correlation functions for several bubble sizes. By adjusting the free parameter, we compare the theoretical correlations with corresponding experimental values and find that the standard deviation associated with their difference can be made as small as 0.017. We discuss the limitations and possible generalizations of our model and conclude by making further physical remarks.