The purpose of this paper is to
prove the following
Theorem: Let ϕ1,ϕ2,⋯ be an infinite sequence of functions in L1([0,2π])
such that L(f) =limn→∞∫02πf(ei𝜃)ϕn(𝜃)d𝜃 exists for every f ∈ H∞.
Then there is a ϕ ∈ L1([0,2π]) such that L(f) =∫02πf(ei𝜃)ϕ(𝜃)d𝜃 for all
f ∈ H∞.