  We study how the Gaussian multiplicative chaos (GMC) measures $\mu^\gamma$
corresponding to the 2D Gaussian free field change when $\gamma$ approaches the
critical parameter $2$. In particular, we show that as $\gamma\to 2^{-}$,
$(2-\gamma)^{-1}\mu^\gamma$ converges in probability to $2\mu'$, where $\mu'$
is the critical GMC measure.
