Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gauge integral
generalized Riemann integral |
| gptkbp:compatibleWith |
countably additive
absolutely convergent |
| gptkbp:definedIn |
real line
|
| gptkbp:defines |
gauge function
|
| gptkbp:extendsTo |
gptkb:Lebesgue_integral
gptkb:Riemann_integral |
| gptkbp:generalizes |
gptkb:Lebesgue_integral
gptkb:Riemann_integral |
| gptkbp:hasProperty |
integral is not always limited to bounded functions
integral is not always limited to continuous functions every Riemann integrable function is Henstock–Kurzweil integrable integral is additive integral is linear integral is not always absolutely convergent integral is not always bounded integral is not always countably additive integral is not always monotone integral is not always sigma-additive integral is not always subadditive integral is not always translation invariant integral is not always limited to measurable functions not a measure in the sense of Lebesgue not limited to measurable functions not monotone not sigma-additive not subadditive not translation invariant satisfies fundamental theorem of calculus can integrate some functions with dense set of discontinuities can integrate derivatives of all continuous functions not every Henstock–Kurzweil integrable function is Lebesgue integrable integral is not always limited to functions with countable discontinuities integral is not always limited to functions with finite discontinuities integral of derivative equals function (under mild conditions) every Lebesgue integrable function is Henstock–Kurzweil integrable |
| gptkbp:heldBy |
finitely additive
|
| https://www.w3.org/2000/01/rdf-schema#label |
Henstock–Kurzweil integral
|
| gptkbp:integratesWith |
functions not Lebesgue integrable
|
| gptkbp:introducedIn |
1950s
|
| gptkbp:namedAfter |
gptkb:Jaroslav_Kurzweil
gptkb:Ralph_Henstock |
| gptkbp:relatedTo |
gptkb:improper_Riemann_integral
|
| gptkbp:usedIn |
real analysis
integration theory |
| gptkbp:bfsParent |
gptkb:Riemann_integral
gptkb:Kurzweil_integral |
| gptkbp:bfsLayer |
6
|