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We provide a general framework and indicate relations between the notions oftransfinite diameter, homogeneous transfinite diameter, and weightedtransfinite diameter for sets in C^N. An ingredient is a formula of Rumelywhich relates the Robin function and the transfinite diameter of a compact set.We also prove limiting formulas for integrals of generalized Vandermondedeterminants with varying weights for a general class of compact sets andmeasures in C^N. Our results extend to certain weights and measures defined oncones in R^N.

Transfinite diameter notions in C^N and integrals of Vandermonde determinants