Saturated measure
Measure in mathematics
In mathematics, a measure is said to be saturated if every locally measurable set is also measurable.[1] A set , not necessarily measurable, is said to be a locally measurable set if for every measurable set of finite measure, is measurable. -finite measures and measures arising as the restriction of outer measures are saturated.
References
- ^ Bogachev, Vladmir (2007). Measure Theory Volume 2. Springer. ISBN 978-3-540-34513-8.
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Measure theory
- Absolute continuity of measures
- Lebesgue integration
- Lp spaces
- Measure
- Measure space
- Probability space
- Measurable space/function
- Almost everywhere
- Atom
- Baire set
- Borel set
- equivalence relation
- Borel space
- Carathéodory's criterion
- Cylindrical σ-algebra
- Cylinder set
- 𝜆-system
- Essential range
- Locally measurable
- π-system
- σ-algebra
- Non-measurable set
- Null set
- Support
- Transverse measure
- Universally measurable
- Atomic
- Baire
- Banach
- Besov
- Borel
- Brown
- Complex
- Complete
- Content
- (Logarithmically) Convex
- Decomposable
- Discrete
- Equivalent
- Finite
- Inner
- (Quasi-) Invariant
- Locally finite
- Maximising
- Metric outer
- Outer
- Perfect
- Pre-measure
- (Sub-) Probability
- Projection-valued
- Radon
- Random
- Regular
- Saturated
- Set function
- σ-finite
- s-finite
- Signed
- Singular
- Spectral
- Strictly positive
- Tight
- Vector
- Carathéodory's extension theorem
- Convergence theorems
- Decomposition theorems
- Egorov's
- Fatou's lemma
- Fubini's
- Hölder's inequality
- Minkowski inequality
- Radon–Nikodym
- Riesz–Markov–Kakutani representation theorem
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