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((Navbox
| name = Measure theory
| title = [[Measure theory]]
| state = (({state|<noinclude>uncollapsed expanded</noinclude><includeonly>autocollapse</includeonly>))}
<!-- | state = (({state|(({1|)))))) -->
| image = 
| bodyclass = hlist
| selected = (({1))}
| above =

 | group1 = Basic concepts
 | list1 =
* [[Absolute continuity]]&nbsp;[[Absolute continuity (measure theory)|of measures]]
* [[Lebesgue integration]]
* [[Lp space|''L''<sup>''p''</sup> spaces]]
* [[Measure (mathematics)|Measure]]
* [[Measure space]]
** [[Probability space]]
* [[Measurable space]]/[[Measurable function|function]]

 | group6 = Sets
 | list6 =
* [[Almost everywhere]]
* [[Atom (measure theory)|Atom]]
* [[Baire set]]
* [[Borel set]]
** [[Borel equivalence relation|equivalence relation]]
* [[Standard Borel space|Borel space]]
* [[Carathéodory's criterion]]
* [[Cylindrical σ-algebra]]
** [[Cylinder set]]
* [[Dynkin system|((lambda))-system]]
* [[Essential range]]
** [[Essential infimum and essential supremum|infimum/supremum]]
* [[Locally measurable set|Locally measurable]]
* [[Pi-system|((pi))-system]]
* [[σ-algebra]]
* [[Non-measurable set]]
** [[Vitali set]]
* [[Null set]]
* [[Support (measure theory)|Support]]
* [[Transverse measure]]
* [[Universally measurable set|Universally measurable]]

 | group10 = Types of [[Measure (mathematics)|Measures]]
 | list10 =
* [[Atomic measure|Atomic]]
* [[Baire measure|Baire]]
* [[Banach measure|Banach]]
* [[Besov measure|Besov]]
* [[Borel measure|Borel]]
* [[Brown measure|Brown]]
* [[Complex measure|Complex]]
* [[Complete measure|Complete]]
* [[Content (measure theory)|Content]]
* ([[Logarithmically concave measure|Logarithmically]])&nbsp;[[Convex measure|Convex]]
* [[Decomposable measure|Decomposable]]
* [[Discrete measure|Discrete]]
* [[Equivalence (measure theory)|Equivalent]]
* [[Finite measure|Finite]]
* [[Inner measure|Inner]]
* ([[Quasi-invariant measure|Quasi-]])&nbsp;[[Invariant measure|Invariant]]
* [[Locally finite measure|Locally finite]]
* [[Maximising measure|Maximising]]
* [[Metric outer measure|Metric outer]]
* [[Outer measure|Outer]]
* [[Perfect measure|Perfect]]
* [[Pre-measure|Pre-measure]]
* ([[Sub-probability measure|Sub-]])&nbsp;[[Probability measure|Probability]]
* [[Projection-valued measure|Projection-valued]]
* [[Radon measure|Radon]]
* [[Random measure|Random]]
* [[Regular measure|Regular]]
** [[Borel regular measure|Borel regular]]
** [[Inner regular measure|Inner regular]]
** [[Outer regular measure|Outer regular]]
* [[Saturated measure|Saturated]]
* [[Set function]]
* [[σ-finite measure|σ-finite]]
* [[s-finite measure|s-finite]]
* [[Signed measure|Signed]]
* [[Singular measure|Singular]]
* [[Spectral measure|Spectral]]
* [[Strictly positive measure|Strictly positive]]
* [[Tightness of measures|Tight]]
* [[Vector measure|Vector]]


 | group15 = [[:Category:Measures (measure theory)|Particular measures]]
 | list15 =
* [[Counting measure|Counting]]
* [[Dirac measure|Dirac]]
* [[Euler measure|Euler]]
* [[Gaussian measure|Gaussian]]
* [[Haar measure|Haar]]
* [[Harmonic measure|Harmonic]]
* [[Hausdorff measure|Hausdorff]]
* [[Intensity measure|Intensity]]
* [[Lebesgue measure|Lebesgue]]
** [[Infinite-dimensional Lebesgue measure|Infinite-dimensional]]
* [[Positive real numbers#Logarithmic measure|Logarithmic]]
* [[Product measure|Product]]
** [[Projection (measure theory)|Projections]]
* [[Pushforward measure|Pushforward]]
* [[Spherical measure]]
* [[Tangent measure|Tangent]]
* [[Trivial measure|Trivial]]
* [[Young measure|Young]]


| group60 = Maps
| list60 = 
* [[Measurable function]]
** [[Bochner measurable function|Bochner]]
** [[Strongly measurable function|Strongly]]
** [[Weakly measurable function|Weakly]]
* Convergence: [[Convergence almost everywhere|almost everywhere]]
* [[Convergence of measures|of measures]]
* [[Convergence in measure|in measure]]
* [[Convergence of random variables|of random variables]]
** [[Convergence in distribution|in distribution]]
** [[Convergence in probability|in probability]]
* [[Cylinder set measure]]
* Random: [[Random compact set|compact set]]
* [[Random element|element]]
* [[Random measure|measure]]
* [[Stochastic process|process]]
* [[Random variable|variable]]
* [[Multivariate random variable|vector]]
* [[Projection-valued measure]]

 | group70 = [[:Category:Theorems in measure theory|Main results]]
 | list70 = 
* [[Carathéodory's extension theorem]]
* Convergence theorems
** [[Dominated convergence theorem|Dominated]]
** [[Monotone convergence theorem|Monotone]]
** [[Vitali convergence theorem|Vitali]]
* Decomposition theorems
** [[Hahn decomposition theorem|Hahn]]
** [[Jordan decomposition theorem|Jordan]]
** [[Maharam's theorem|Maharam's]]
* [[Egorov's theorem|Egorov's]]
* [[Fatou's lemma]]
* [[Fubini's theorem|Fubini's]]
** [[Fubini–Tonelli theorem|Fubini–Tonelli]]
* [[Hölder's inequality]]
* [[Minkowski inequality]]
* [[Radon–Nikodym theorem|Radon–Nikodym]]
* [[Riesz–Markov–Kakutani representation theorem]]

 | group80 = Other results
 | list80 = 
((Navbox|subgroup
| group1 =
| list1  =
* [[Disintegration theorem]]
** [[Lifting theory]]
* [[Lebesgue's density theorem]]
* [[Lebesgue differentiation theorem]]
* [[Sard's theorem]]
* [[Vitali–Hahn–Saks theorem]]
| group2 = ((small|For [[Lebesgue measure]]))
| list2  = 
* [[Isoperimetric inequality]]
* [[Brunn–Minkowski theorem]]
** [[Milman's reverse Brunn–Minkowski inequality|Milman's reverse]]
* [[Minkowski–Steiner formula]]
* [[Prékopa–Leindler inequality]]
* [[Vitale's random Brunn–Minkowski inequality]]
))

 | group90 = Applications&nbsp;&amp;&nbsp;related
 | list90 = 
* [[Convex analysis]]
* [[Descriptive set theory]]
* [[Probability theory]]
* [[Real analysis]]
* [[Spectral theory]]

))<noinclude>
((Documentation
 | content =
((Collapsible option |statename=optional))
))
[[Category:Mathematics navigational boxes]]
</noinclude>

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