Pseudomeromorphic currents on subvarieties

Let $i\colon X \to Y$ be pure-dimensional reduced subvariety of a smooth manifold $Y$. We prove that the direct image of pseudomeromorphic currents on $X$ are pseudomeromorphic on $Y$. We also prove a partial converse: if $i_*τ$ is pseudomeromorphic and has the standard extension property, then $τ$ is pseudomermorphic on $X$.

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