  Let $M_{\gamma}$ be a subcritical Gaussian multiplicative chaos measure
associated with a general log-correlated Gaussian field defined on a bounded
domain $D \subset \mathbb{R}^d$, $d \geq 1$. We find an explicit formula for
its singularity spectrum by showing that $M_{\gamma}$ satisfies almost surely
the multifractal formalism, i.e., we prove that its singularity spectrum is
almost surely equal to the Legendre-Fenchel transform of its $L^q$-spectrum.
Then, applying this result, we compute the lower singularity spectrum of the
multifractal random walk and of the Liouville Brownian motion.
