  Approximable algebras were defined by Chen in his proof of the Fujita theorem
in the arithmetic context. These were shown to not be necessarily subalgebras
of section rings of big line bundles in a previous prepreint of the author.
Here, we show that whilst approximable algebras are not necessarily subalgebras
of section rings of big line bundles, they are necessarily subalgebras of
section rings of infinite sums of Weil divisors.
