Measure Spaces (π,π΄,π)
- a type ofΒ mathematical space
- is aΒ measurable space (π,π΄) with aΒ measure (π)
- is a tripleΒ (π,π΄,π)Β where:
- πΒ is a set
- π΄Β is aΒ Ο-algebraΒ on the set π
- πΒ is aΒ measureΒ onΒ (π,π΄)
- is a basic mathematical object of measure theory
Measure Spaces - Types
The most important classes of measure spaces are defined by the properties of their associated measures. This includes:
|
Probability Spaces (Sample Space - Event Space - Probability Measure) |
is a measure space where the measure is aΒ probability measure |
|---|---|
|
Finite Measure Spaces |
is a measure space where the measure is aΒ finite measure |
|
Ο-Finite Measure Spaces |
is a measure space where the measure is a Ο-finite measure |
|
is a measure space in which every subset of every null set is measurable (having measure zero) |