Category:Measure Theory
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This category contains results about Measure Theory.
Definitions specific to this category can be found in Definitions/Measure Theory.
Measure theory is the subfield of analysis concerned with the properties of measures, particularly the Lebesgue measure.
Subcategories
This category has the following 55 subcategories, out of 55 total.
A
C
- Convergence in Mean (1 P)
- Convergence in Measure (2 P)
- Countably Additive Functions (2 P)
D
- Dynkin Systems (8 P)
F
- Fatou's Lemma (3 P)
- Fatou's Lemma for Integrals (3 P)
- Fatou's Lemma for Measures (4 P)
- Finitely Additive Functions (1 P)
H
- Horizontal Section of Functions (12 P)
I
- Inner Jordan Content (empty)
J
L
- Lebesgue Integrals (empty)
- Lebesgue Measure (10 P)
M
- Markov's Inequality (2 P)
N
- Negative Parts (13 P)
O
- Outer Jordan Content (3 P)
P
- Positive Parts (13 P)
- Pre-Measures (5 P)
R
- Reverse Fatou's Lemma (3 P)
S
- Scheffé's Lemma (2 P)
- Stieltjes Functions (2 P)
T
V
- Vertical Section of Functions (12 P)
- Vertical Section of Sets (11 P)
- Vitali Set Existence Theorem (4 P)
- Vitali Sets (2 P)
Y
Pages in category "Measure Theory"
The following 94 pages are in this category, out of 94 total.
A
C
- Carathéodory's Theorem (Measure Theory)
- Carathéodory's Theorem (Measure Theory)/Corollary
- Characteristic Function of Null Set is A.E. Equal to Zero
- Characterization of Almost Everywhere Zero
- Characterization of Essentially Bounded Functions
- Characterization of Integrable Functions
- Characterization of Measures
- Composition of Measurable Mappings is Measurable
- Continuity under Integral Sign
- Continuous Composition of Measurable Functions into Second Countable Space is Measurable
- Convergence a.u. Implies Convergence a.e.
- Convergence in Norm Implies Convergence in Measure
- Convergence in Sigma-Finite Measure
- Convolution of Integrable Function with Bounded Function
- Convolution of Measurable Function and Measure is Bilinear
- Convolution of Measurable Functions is Bilinear
- Countable Union of Measurable Sets as Disjoint Union of Measurable Sets
- Countably Additive Function also Finitely Additive
- Cover of Interval By Closed Intervals is not Pairwise Disjoint
E
F
- Factorization Lemma
- Factorization Lemma for Extended Real-Valued Functions
- Factorization Lemma for Real-Valued Functions
- Factorization Lemma/Extended Real-Valued Function
- Factorization Lemma/Real-Valued Function
- Fatou's Lemma for Integrals
- Fatou's Lemma for Integrals/Integrable Functions
- Fatou's Lemma for Integrals/Positive Measurable Functions
- Fatou's Lemma for Measures
- Finite Hausdorff Measure Implies Zero Higher Dimensional Measure
- Functions A.E. Equal iff Positive and Negative Parts A.E. Equal
I
- Inner Jordan Content is Monotone
- Inner Limit in Hausdorff Space by Open Neighborhoods
- Inner Limit in Hausdorff Space by Set Closures
- Integrable Function is A.E. Real-Valued
- Integrable Function with Zero Integral on Sub-Sigma-Algebra is A.E. Zero
- Integrable Function with Zero Integral on Sub-Sigma-Algebra is A.E. Zero/Proof 2
- Integrable Functions with Equal Integrals on Sub-Sigma-Algebra are A.E. Equal
- Integral of Distribution Function
J
L
M
- Mapping between Euclidean Spaces Measurable iff Components Measurable
- Mapping Measurable iff Measurable on Generator
- Markov's Inequality
- Measurable Function is Integrable iff A.E. Equal to Real-Valued Integrable Function
- Measurable Function is Simple Function iff Finite Image Set/Corollary
- Measurable Functions with Equal Integrals on Sub-Sigma-Algebra are A.E. Equal
- Measurable Image
- Measurable Mappings from Product Measurable Space
- Measurable Mappings to Product Measurable Space
- Measure of Stieltjes Function of Measure
- Minkowski's Inequality for Double Integrals
- Monotone Convergence Theorem (Measure Theory)
- Monotone Convergence Theorem (Measure Theory)/Corollary
- Monotone Convergence Theorem for Positive Simple Functions
S
- Scheffé's Lemma
- Series of Positive Measurable Functions is Positive Measurable Function
- Sigma-Algebras with Independent Generators are Independent
- Simple Function has Standard Representation
- Standard Machinery
- Stieltjes Function of Measure is Stieltjes Function
- Stieltjes Function of Measure of Finite Stieltjes Function
- Strictly Positive Hausdorff Measure implies Infinite Lower Dimensional Measure