28-XX 
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Measure and integration
{For analysis on manifolds, see
58-XX }
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28-00
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General reference works (handbooks, dictionaries, bibliographies, etc.)
|
|
28-01
|
Instructional exposition (textbooks, tutorial papers, etc.)
|
|
28-02
|
Research exposition (monographs, survey articles)
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|
28-03
|
Historical {!must also be assigned at least one classification number from section 01}
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|
28-04
|
Explicit machine computation and programs (not the theory of computation or programming)
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|
28-06
|
Proceedings, conferences, collections, etc.
|
|
28Axx
|
Classical measure theory
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|
28A05
|
Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
[See also
03E15 ,
26A21 ,
54H05 ]
|
|
28A10
|
Real- or complex-valued set functions
|
|
28A12
|
Contents, measures, outer measures, capacities
|
|
28A15
|
Abstract differentiation theory, differentiation of set functions
[See also
26A24 ]
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|
28A20
|
Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
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|
28A25
|
Integration with respect to measures and other set functions
|
|
28A33
|
Spaces of measures, convergence of measures
[See also
46E27 ,
60Bxx ]
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|
28A35
|
Measures and integrals in product spaces
|
|
28A50
|
Integration and disintegration of measures
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|
28A51
|
Lifting theory
[See also
46G15 ]
|
|
28A60
|
Measures on Boolean rings, measure algebras
[See also
54H10 ]
|
|
28A75
|
Length, area, volume, other geometric measure theory
[See also
26B15 ,
49Q15 ]
|
|
28A78
|
Hausdorff and packing measures
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|
28A80
|
Fractals
[See also
37Fxx ]
|
|
28A99
|
None of the above, but in this section
|
|
28Bxx
|
Set functions, measures and integrals with values in abstract spaces
|
|
28B05
|
Vector-valued set functions, measures and integrals
[See also
46G10 ]
|
|
28B10
|
Group- or semigroup-valued set functions, measures and integrals
|
|
28B15
|
Set functions, measures and integrals with values in ordered spaces
|
|
28B20
|
Set-valued set functions and measures; integration of set-valued functions; measurable selections
[See also
26E25 ,
54C60 ,
54C65 ,
91B14 ]
|
|
28B99
|
None of the above, but in this section
|
|
28Cxx
|
Set functions and measures on spaces with additional structure
[See also
46G12 ,
58C35 ,
58D20 ]
|
|
28C05
|
Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
|
|
28C10
|
Set functions and measures on topological groups, Haar measures, invariant measures
[See also
22Axx ,
43A05 ]
|
|
28C15
|
Set functions and measures on topological spaces (regularity of measures, etc.)
|
|
28C20
|
Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
[See also
46G12 ,
58C35 ,
58D20 ,
60B11 ]
|
|
28C99
|
None of the above, but in this section
|
|
28Dxx
|
Measure-theoretic ergodic theory
[See also
11K50 ,
11K55 ,
22D40 ,
47A35 ,
54H20 ,
37Axx ,
60Fxx ,
60G10 ]
|
|
28D05
|
Measure-preserving transformations
|
|
28D10
|
One-parameter continuous families of measure-preserving transformations
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|
28D15
|
General groups of measure-preserving transformations
|
|
28D20
|
Entropy and other invariants
|
|
28D99
|
None of the above, but in this section
|
|
28Exx
|
Miscellaneous topics in measure theory
|
|
28E05
|
Nonstandard measure theory
[See also
03H05 ,
26E35 ]
|
|
28E10
|
Fuzzy measure theory
[See also
03E72 ,
26E50 ,
94D05 ]
|
|
28E15
|
Other connections with logic and set theory
|
|
28E99
|
None of the above, but in this section
|