By Zhao W., Liu P.

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3. 5). Let (zi )i∈N ⊂ RN and consider the measures µi := |x − zi |−2a dx, then we have for 0 < r < 2 as r → 0 8 |y − zi |−bp sup x∈B2 (0), i∈N Br (x) |x−y| s ds dy → 0. µi (Bs (x)) Proof. We use as c a generic constant that may change its value from line to line. Fix x ∈ B2 (0). From the doubling property of the measure µi (see [12]) we find 8 Mi (x, |x − y|) := |x−y| ≤c s ds µi (Bs (x)) |x − y|−N +2a+2 , if |x − y| > 12 |x − zi | |x − y|−N +2 |x − zi |2a + |x − zi |−N +2a+2 , if |x − y| ≤ 21 |x − zi |.

Gi zK(0) (rui (xi )2/(N −2−2a) )− 2 + r( gi ) zK(0) DEGENERATE CRITICAL ELLIPTIC EQUATIONS 31 Since for Cui (xi )−2/(N −2−2a) ≤ r ≤ ri , there results C ≤ rui (xi )2/(N −2−2a) ≤ Ri , we have that d gi ≤ εi . gi ≤ εi , dr ∂B ∂B 2/(N −2−2a) (0) 2/(N −2−2a) (0) rui (xi ) rui (xi ) 1+δ K(0) Moreover for C = 2 (p−2)(N −2−2a) p(N −2−2a) − 2 Choosing εi = o Ri we have 1 − K(0)ui (xi )p−2 r (p−2)(N −2−2a) 2 ≤ −δ. ✷ the claim follows. 3. 5). Let (zi )i∈N ⊂ RN and consider the measures µi := |x − zi |−2a dx, then we have for 0 < r < 2 as r → 0 8 |y − zi |−bp sup x∈B2 (0), i∈N Br (x) |x−y| s ds dy → 0.

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### A Biplurisubharmonic Characterization of AUMD Spaces by Zhao W., Liu P.

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