= Bernstein growth dimension of a Weyl algebra module
{c}
{title2=$d(M)=\deg(\dim_\mathbb C F_jA_nM_0)$}
For a nonzero finitely generated <Weyl algebra> <module>, choose a finite-dimensional generating subspace $M_0$. Under the <Bernstein filtration>, $\dim(F_jA_nM_0)$ is eventually polynomial because the graded <module> is finite over a polynomial ring. Its degree is independent of the generating subspace, since two generating filtrations bound each other after fixed shifts. It equals the <Gelfand–Kirillov dimension of a module>.
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