Cartan's lemma (potential theory)
In potential theory, a branch of mathematics, Cartan's lemma, named after Henri Cartan, is a bound on the measure and complexity of the set on which a logarithmic Newtonian potential is small.The following statement can be found in Levin's book.
Let μ be a finite positive Borel measure on the complex plane C with μ = n. Let u be the logarithmic potential of μ:
Given H ∈ , there exist discs of radius ri such that
and
for all z outside the union of these discs.
