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We introduce the notion of (p, r)-null sequences in a Banach space and we prove a Grothendieck-like result: a subset of a Banach space is relatively (p, r)-compact if and only if it is contained in the closed convex hull of a (p, r)-null sequence. This extends a recent description of relatively p-compact sets due to Delgado and Piñeiro, providing to it an alternative straightforward proof.

A description of relatively (p; r)-compact sets