  A multiple integral representation of single and joint moments of the total
mass of the limit log-infinitely divisible stochastic measure of Bacry and Muzy
[$\textit{Comm. Math. Phys.}$ ${\bf 236}$: 449-475, 2003] is derived. The
covariance structure of the total mass of the measure is shown to be
logarithmic. A generalization of the Selberg integral corresponding to single
moments of the limit measure is proposed and shown to satisfy a recurrence
relation. The joint moments of the limit lognormal measure, classical Selberg
integral with $\lambda_1=\lambda_2=0,$ and Morris integral are represented in
the form of multiple binomial sums. For application, low moments of the limit
log-Poisson measure are computed exactly and low joint moments of the limit
lognormal measure are considered in detail.
