Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:analysis
|
| gptkbp:assigns_to_empty_set |
gptkb:0
|
| gptkbp:assigns_to_interval |
length of the interval
|
| gptkbp:can_be_extended_by |
Lebesgue outer measure
|
| gptkbp:defined_on |
real numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lebesgue measure
|
| gptkbp:is_a |
Borel measure
Borel sigma-algebra real-valued function finite measure generalization of length measure on Euclidean space measure theory concept set function sigma-finite measure |
| gptkbp:is_applied_in |
functional analysis
|
| gptkbp:is_characterized_by |
measurable sets
|
| gptkbp:is_complete |
gptkb:true
|
| gptkbp:is_countably_additive |
gptkb:true
|
| gptkbp:is_defined_by |
Lebesgue measurable sets
n-dimensional space Carathéodory criterion Lebesgue outer measure outer measure |
| gptkbp:is_in |
L^p spaces
|
| gptkbp:is_not_countably_additive |
for non-measurable sets
|
| gptkbp:is_not_defined_for |
non-measurable sets
|
| gptkbp:is_not_finite |
for unbounded sets
|
| gptkbp:is_related_to |
Borel measure
Fubini's theorem Lebesgue measurable functions Lebesgue integral Lebesgue spaces Lebesgue differentiation theorem measure zero sets |
| gptkbp:is_translation_invariant |
gptkb:true
|
| gptkbp:is_used_in |
gptkb:topology
gptkb:analysis gptkb:Quantum_Mechanics gptkb:statistical_mechanics probability theory differential equations functional analysis functional spaces real analysis real-valued functions |
| gptkbp:is_used_to |
prove theorems in analysis
define measurable functions |
| gptkbp:bfsParent |
gptkb:Georg_Cantor
|
| gptkbp:bfsLayer |
4
|