Uniform law of large numbers (ULLN)

A class

G

satisfies a uniform law of large numbers when its empirical means converge uniformly to their expectations:

sup_{g \in G} ∣ P_{n} g - P g ∣ \to 0.

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- Glivenko-Cantelli theorem Uniform law of large numbers

Glivenko-Cantelli theorem

The empirical distribution function converges uniformly almost surely to the population distribution function.

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Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 210 / 1 / a / Solution

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