I am reading the slicing measure section in Evans's book "Weak convergence methods for nonlinear PDEs", and I was wondering why is the proof need to approximate $f\in C_c(\mathbb{R}^m)$ by a sequence of $f_k$ to only get to the point of defining $f\mapsto \Gamma_x(f)$ is bounded linear continuous, why don't we just start from $f$ and define $\Gamma_x(f)$ as the density of the measure induced by $f$ with respect to $\sigma$?
2026-03-26 00:59:56.1774486796
Question about slicing measures - weak convergence methods for nonlinear PDEs
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