Questions tagged [empirical-processes]

From https://en.wikipedia.org/wiki/Vapnik–Chervonenkis_theory Let $X_1, ..., X_n$ be a random sample from a probability distribution P. Let $$P_nf=\frac{1}{n}\sum_{i=1}^nf(X_i), \quad Pf=\int fdP.$$ A class ${F}$ of measurable functions $f$ is…

Question: My question about the theorem Glivenko-Cantelli (GC) by bracketing is: if $N_{[]}(\varepsilon,\mathcal{F},L_{1}(P))=\infty$, which part of the above proof will fail, thus GC will fail. Source: the theorem and the proof are directly from:…