Semipolar sets and intrinsic Hausdorff measure

2017/11/24 by Hansen, Wolfhard, Netuka, Ivan
#28A78 #31C12 #31C15 #31D05 #31E05 #35J08 #35K08 #60J45 #60J60 #60J75 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.08918

Abstract

Given a "Green function" G on a locally compact space X with countable base, a Borel set A in X is called G-semipolar, if there is no measure ν≠ 0 supported by A such that Gν:=∫ G(⋅,y) dν(y) is a continuous real function on X. Introducing an intrinsic Hausdorff measure m_G using G-balls B(x,ρ):=\y∈ X\colon G(x,y)>1/ρ\, it is shown that every set A in X with m_G(A)

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