Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
indicator function nowhere continuous function |
| gptkbp:alsoKnownAs |
gptkb:Dirichlet's_function
|
| gptkbp:category |
counterexample in analysis
|
| gptkbp:codomain |
real numbers
|
| gptkbp:definedIn |
real numbers
|
| gptkbp:defines |
f(x) = 1 if x is rational, f(x) = 0 if x is irrational
|
| gptkbp:domain |
real numbers
|
| gptkbp:graphics |
dense in the plane
|
| https://www.w3.org/2000/01/rdf-schema#label |
Dirichlet function
|
| gptkbp:namedAfter |
gptkb:Peter_Gustav_Lejeune_Dirichlet
|
| gptkbp:property |
Lebesgue integrable on any interval
discontinuous everywhere not Riemann integrable on any interval |
| gptkbp:usedIn |
real analysis
|
| gptkbp:valueAtIrrational |
0
|
| gptkbp:valueAtRational |
1
|
| gptkbp:bfsParent |
gptkb:Peter_Gustav_Lejeune_Dirichlet
|
| gptkbp:bfsLayer |
5
|