Regularity and Hölder continuity of weighted $m$-subharmonic measures

In this talk, we investigate weighted $m$-subharmonic measures within the class of $m$-subharmonic functions. We establish several results concerning $(m,\psi)$-regularity. In particular, we show that if the weighted $(m,\psi)$-subharmonic measure is Hölder continuous with respect to a compact set, then it remains Hölder continuous in $D$. This result is new even in the unweighted case.