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We study the Lelong classes $\mathcal{L}(V),\mathcal{L}^+(V)$ of pshfunctions on an affine variety $V$. We compute the Monge-Amp\`ere mass of thesefunctions, which we use to define the degree of a polynomial on $V$ in terms ofpluripotential theory (the Lelong degree). We compute the Lelong degreeexplicitly in a specific example. Finally, we derive an affine version ofB\'ezout's theorem.

Lelong classes of plurisubharmonic functions on an affine variety