In this article we will first prove a result about the convergence in capacity. Next we will obtain a general decomposition theorem for complex Monge-Ampère measures which will be used to prove a comparison principle for the complex Monge-Ampère operator.

ABSTRACT. In this paper we study q-subharmonic and q-plurisubharmonic functions in C n . Next as an application, we give the notion of q-convex domains in C n which is an extension of weakly q-convex domains introduced and investigated in [10]. In the end of the paper we show that the q-convexity is the local property and give some examples about q-convex domains.

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Let E be a Frechet (resp. Frechet-Hilbert) space. It is shown DN )). Moreover it is also shown that E ∈ (DN ) if and only if H b (E ) ∈ (DN ). In the nuclear case these results were proved by Meise and Vogt [2].

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