Continuous approximation of quasi-plurisubharmonic functions

Let $X$ be a compact Kähler manifold and $θ$ a smooth closed $(1,1)$-real form representing a big cohomology class $α\in H^{1,1}(X,\R)$. The purpose of this note is to show, using pluripotential and viscosity techniques, that any $θ$-plurisubharmonic function $\f$ can be approximated from above by a decreasing sequence of continuous $θ$-plurisubharmonic functions with minimal singularities, assuming that there exists a single such function.

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