  We define $p$-adic BPS or $p$BPS-invariants for moduli spaces
$M_{\beta,\chi}$ of 1-dimensional sheaves on del Pezzo surfaces by means of
integration over a non-archimedean local field $F$ . Our definition relies on a
canonical measure $\mu_{can}$ on the $F$-analytic manifold associated to
$M_{\beta,\chi}$ and the $p$BPS-invariants are integrals of natural
$\mathbb{G}_m$-gerbes with respect to $\mu_{can}$. A similar construction can
be done for meromorphic Higgs bundles on a curve.
  Our main theorem is a $\chi$-independence result for these $p$BPS-invariants.
For 1-dimensional sheaves on del Pezzo surfaces and meromorphic Higgs bundles,
we obtain as a corollary the agreement of $p$BPS with usual BPS-invariants
trough a result of Maulik-Shen.
