In this paper we study relations between the weighted energy class E χ introduced by S. Benelkourchi, V. Guedj and A. Zeriahi recently with Cegrell's classes E and N . Next we establish a generalized comparison principle for the operator M χ . As an application, we prove a version of existence of solutions of Monge-Ampère type equations in the class E χ (H, ).
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