Weyl's equidistribution theorem
GPTKB entity
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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
|