Weyl's equidistribution theorem

GPTKB entity

Statements (16)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo sequences of real numbers
gptkbp:field analysis
number theory
https://www.w3.org/2000/01/rdf-schema#label Weyl's equidistribution theorem
gptkbp:implies uniform distribution mod 1
gptkbp:namedAfter gptkb:Hermann_Weyl
gptkbp:relatedTo gptkb:Kronecker's_theorem
gptkb:discrepancy_theory
ergodic theory
gptkbp:sentence If (x_n) is a sequence such that the fractional parts of x_n are uniformly distributed mod 1, then for any interval [a, b] in [0,1), the proportion of terms in [a, b] approaches b-a as n goes to infinity.
gptkbp:usedIn gptkb:Diophantine_approximation
gptkb:quasi-Monte_Carlo_methods
gptkbp:yearProposed 1916
gptkbp:bfsParent gptkb:Hermann_Weyl
gptkbp:bfsLayer 4