compact Hausdorff space $X$; the sup-norm algebra $C(X)$ of all complex-valued continuous functions on $X$; its closed subalgebras (called function algebras); measure orthogonal to a function algebra
In the present note, we characterize the essential set of a function algebra defined on a compact Hausdorff space $X$ in terms of its orthogonal measures on $X$.
 Hoffman K., Singer I.M.: Maximal algebras of continuous functions
. Acta Math. 103 (1960), 217-241. MR 0117540
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