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of the location of the interval itself (but it is dependent on the interval size ), so long as the interval is contained in the distribution's support.

Indeed, if and if is a subinterval of with fixed then:

which is independent of This fact motivates the distribution's name.

Uniform distribution on more general sets

The uniform distribution can be generalized to sets more general than intervals.

Formally, let be a Borel set of positive, finite Lebesgue measure

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