  Given a compact set $K$ one may define a transfinite diameter for $K$ via a
limiting process involving maximising a Vandermonde determinant over $K$ with
respect to a monomial basis. Different transfinite diameters may be obtained by
using different polynomial bases in the Vandermonde determinant calculation. We
show that if these bases are sufficiently similar that the transfinite diameter
of $K$ is unchanged. Utilising this result we show that the transfinite
diameters defined by Cox-Ma`u and Berman-Boucksom for algebraic varieties are
equal.
