For bounded real-valued function classes, uniform convergence at scale γ, agnostic learnability at γ/2, and finite fat-shattering dimension above γ are equivalent.
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Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale
For bounded real-valued function classes, uniform convergence at scale γ, agnostic learnability at γ/2, and finite fat-shattering dimension above γ are equivalent.