Definition 4.17 . [05B0]
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Definition 4.17.
Let be a complete, non-archimedean, non-trivially valued field, a strictly -analytic space and a line bundle on . A continuous metric on is called locally semipositive if for any there is an open neighbourhood of such that is a uniform limit of semipositive piecewise -linear metrics on . It is called locally potentially semipositive if its base change to the completion of an algebraic closure of is locally semipositive. If is an open subset of for a separated scheme of finite type over then using the Remarks 4.14 and 4.16 we define the Monge-Ampère measure for locally potentially semipositive metrized line bundles on .