### Quick description

If is a sequence mod 1, such that is uniformly distributed modulo 1 for all non-zero h, then is also uniformly distributed modulo 1.

### Prerequisites

Undergraduate analysis

### Example 1

(Equidistribution of polynomials)

### Example 2

(Multiple recurrence in weakly mixing systems)

### General discussion

A quantitative version of this fact, known as *van der Corput's inequality*, is also useful.

(Also mention Bergelson's Hilbert space version.)

Not to be confused with the van der Corput lemma for oscillatory integrals.

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