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In this paper, we collect some fundamental properties of the arithmeticrestricted volumes (or the arithmetic multiplicities) of the adelicallymetrized line bundles. The arithmetic restricted volume has the concavityproperty and characterizes the arithmetic augmented base locus as the nulllocus. We also show a generalized Fujita approximation for the arithmeticrestricted volumes.

Remarks on the arithmetic restricted volumes and the arithmetic base loci