Mergelyan-Wesler Theorem

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Theorem

Let $P = \sequence {D_1, D_2, \dotsc}$ be an infinite sequence of disjoint open disks whose union is the unit disk $D$ except for a set of measure zero.

Let $r_n$ be the radius of $D_n$.

Then:

$\displaystyle \sum_{k \mathop = 1}^\infty r_k = +\infty$


Proof


Source of Name

This entry was named for Sergey Nikitovich Mergelyan and Oscar Wesler.


Sources