Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
Devil's staircase
|
| gptkbp:builtBy |
using ternary expansion
|
| gptkbp:category |
mathematical analysis
fractal geometry |
| gptkbp:constantOn |
complement of Cantor set
|
| gptkbp:continuity |
true
|
| gptkbp:definedIn |
[0,1]
|
| gptkbp:describedYear |
1883
|
| gptkbp:differentiable |
almost nowhere
|
| gptkbp:example |
fractal function
singular function |
| gptkbp:firstDescribed |
gptkb:Georg_Cantor
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cantor function
|
| gptkbp:LebesgueMeasureOfIncreaseSet |
0
|
| gptkbp:mapType |
Cantor set to [0,1]
|
| gptkbp:monotonic |
non-decreasing
|
| gptkbp:notableDerivative |
0 almost everywhere
|
| gptkbp:range |
[0,1]
|
| gptkbp:shape |
staircase-like
|
| gptkbp:totalVariation |
1
|
| gptkbp:usedIn |
gptkb:probability_theory
measure theory real analysis |
| gptkbp:bfsParent |
gptkb:Richard_Cantor
|
| gptkbp:bfsLayer |
7
|