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I wish to show that a function which is "essentially constant" (defined shortly) can't be a good classifier (machine learning). For this i need to estimate the "complexity" of such a class of ...

For some $L>0$ say ${\cal L}$ is the space of all $L-$Lipschitz functions mapping $(X,\rho) \rightarrow [0,1]$ where $(X,\rho)$ is a metric space. For any $\alpha >0$ do we know of a ...