A disk algebra is an algebra of functions which are analytic on the open unit disk in
and continuous up to the boundary. A
representative measure for a point 
in the closed disk is a nonnegative
measure 
such that 
for all 
in 
.
These measures form a compact, convex
set 
in the linear space of all measures.
Stated another way, let 
denote the closed unit disk 
. Suppose that 
denoted the set of all elements of 
which are analytic on the interior of 
. 
is a closed subalgebra of 
and so is a unital commutative Banach
algebra. This algebra is called the disk algebra.
