Integration

Start reading → Inequalities of convexity

1. Front matter
   1. Introduction
   2. To the reader
   3. To the reader
2. IInequalities of convexity
   1. Inequalities of convexity
   2. Historical Note
3. IIRiesz spaces
   1. Riesz spaces
   2. § 1. Riesz spaces and fully lattice-ordered spaces16
   3. § 2. Linear forms on a Riesz space13
4. IIIMeasures on locally compact spaces
   1. Measures on locally compact spaces
   2. § 1. Measures on a locally compact space41
   3. § 2. Support of a measure26
   4. § 3. Integrals of continuous vector-valued functions17
   5. § 4. Products of measures22
5. IVExtension of a measure. Lp spaces
   1. Extension of a measure. Lp spaces
   2. § 1. Upper integral of a positive function34
   3. § 2. Negligible functions and sets15
   4. § 3. LP spaces44
   5. § 4. Integrable functions and sets63
   6. § 5. Measurable functions and sets79
   7. § 6. Convexity inequalities22
   8. § 7. Barycenters31
6. VIntegration of measures
   1. Integration of measures
   2. § 1. Essential upper integral22
   3. § 2. Summable families of positive measures12
   4. § 3. Integration of positive measures30
   5. § 4. Integration of positive point measures10
   6. § 5. Measures defined by numerical densities52
   7. § 6. Images of a measure29
   8. § 7. Integration with respect to an induced measure20
   9. § 8. Products of measures31
   10. Historical Note
7. VIVectorial integration
   1. Vectorial integration
   2. § 1. Integration of vector-valued functions34
   3. § 2. Vectorial measures . "42
   4. § 3. Disintegration of measures16
   5. App. 0. Complements on topological vector spaces6
   6. Historical Note
8. VIIHaar measure
   1. Haar measure
   2. § 1. Construction of a Haar measure42
   3. § 2. Quotient of a space by a group; homogeneous spaces53
   4. § 3. Applications and examples24
   5. App. 1. 1
   6. App. 2.
9. VIIIConvolution and representations
   1. Convolution and representations
   2. § 1. Convolution13
   3. § 2. Linear representations of groups22
   4. § 3. Convolution of measures on groups16
   5. § 4. Convolution of measures and functions38
   6. § 5. The space of closed subgroups20
   7. Historical Note
10. IXMeasures on Hausdorff topological spaces
    1. Measures on Hausdorff topological spaces
    2. § 1. Premeasures and measures on a topological space52
    3. § 2. Operations on measures41
    4. § 3. Measures and additive set functions17
    5. § 4. Inverse limits of measures7
    6. § 5. Measures on completely regular spaces33
    7. § 6. Promeasures and measures on a locally convex space33
    8. App. 0. Complements on Hilbert spaces5
    9. Historical Note
11. Indexes
    1. Index of notations
    2. Index of notations
    3. Index of terminology
    4. Index of terminology