Lelong classes of plurisubharmonic functions on an affine variety

We study the Lelong classes L(V),L+(V) of psh functions on an affine variety V. We compute the Monge-Ampère mass of these functions, which we use to define the degree of a polynomial on V in terms of pluripotential theory (the Lelong degree). We compute the Lelong degree explicitly in a specific example. Finally, we derive an affine version of Bézout’s theorem.