Continuity of Monge–Ampère Potentials in Big Cohomology Classes

Extending DiNezza-Lu's approach to the setting of big cohomology classes, we prove that solutions degenerate complex Monge-Amp{\`e}re equations on compact K{\"a}hler manifolds are continuous a Zariski open set. This allows us show singular K{\"a}hler-Einstein metrics log canonical varieties general type have potentials ample locus outside non-klt part.