Weighted $m$-subharmonic measures

In this talk, we study weighted $m$-subharmonic measures within the class of $m$-subharmonic functions. We investigate their fundamental properties and establish several theorems concerning $(m,\psi)$-regularity. In particular, we prove that if the weighted $(m,\psi)$-subharmonic measure is Hölder continuous with respect to a compact set, then it is also Hölder continuous in $D$; this result is new even in the unweighted case. We furthermore introduce the notions of $(m,\psi)$-capacity and weighted $\mathcal{P}_{(m,\psi)}$-capacity and establish their basic properties.