Let 1 <= m <= n be fixed integers. Let Omega subset of C-n be a bounded m-hyperconvex domain and A subset of Omega x]0, +infinity[ a finite set of weighted poles. We define and study properties of the m-subharmonic Green function of Omega with prescribed behavior near the weighted set A. In particular we prove uniform continuity of the exponential Green function in both variables (z, A) in the metric space (Omega) over bar x F, where F is a suitable family of sets of weighted poles in Omega x ]0, +infinity[ endowed with the Hausdorff distance. Moreover, we give a precise estimate on its modulus of continuity. Our results generalize and improve previous results concerning the pluricomplex Green function due to P. Lelong.
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