Difference between revisions of "Site projects:Patrolling measure theory/Task list"
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| − | + | * [[A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections]] | |
| + | * [[A function is a measure iff it measures the empty set as 0, disjoint sets add, and it is continuous from below (with equiv. conditions)]] | ||
| + | * [[A map from two sigma-algebras, A and B, is measurable if and only if for some generator of B (call it G) we have the inverse image of S is in A for every S in G]] | ||
| + | * [[Additive function]] | ||
| + | * [[Algebra (Disambiguation)]] | ||
| + | * [[Algebra of sets]] | ||
| + | * [[Borel sigma-algebra]] | ||
| + | * [[Borel sigma-algebra generated by]] | ||
| + | * [[Class of sets closed under complements properties]] | ||
| + | * [[Class of sets closed under set-subtraction properties]] | ||
| + | * [[Class of smooth real-valued functions on R-n]] | ||
| + | * [[Class of smooth real-valued functions on R-n/Structure]] | ||
| + | * [[Classes of continuously differentiable functions]] | ||
| + | * [[Composition of measurable maps is measurable]] | ||
| + | * [[Conditions for a Dynkin system to be a sigma-algebra]] | ||
| + | * [[Conditions for a generated Dynkin system to be a sigma-algebra]] | ||
| + | * [[Conditions for a map to be a measurable map]] | ||
| + | * [[D-system]] | ||
| + | * [[Derivative]] | ||
| + | * [[Dynkin system]] | ||
| + | * [[Dynkin system generated by]] | ||
| + | * [[Dynkin system/Definition 1]] | ||
| + | * [[Dynkin system/Definition 2]] | ||
| + | * [[Dynkin system/Proof that definitions 1 and 2 are equivalent]] | ||
| + | * [[Extended real value]] | ||
| + | * [[Function terminology]] | ||
| + | * [[Generator]] | ||
| + | * [[Generator (sigma-algebra)]] | ||
| + | * [[Index of common sigma-algebras]] | ||
| + | * [[Integral]] | ||
| + | * [[Integral (measure theory)]] | ||
| + | * [[Integral of a positive function (measure theory)]] | ||
| + | * [[Integral of a positive function (measure theory)/Definition]] | ||
| + | * [[Integral of a simple function (measure theory)]] | ||
| + | * [[Integral of a simple function (measure theory)/Definition]] | ||
| + | * [[Lebesgue measure]] | ||
| + | * [[Limit of increasing sequence of sets]] | ||
| + | * [[Measurable function]] | ||
| + | * [[Measurable map]] | ||
| + | * [[Measurable space]] | ||
| + | * [[Measure]] | ||
| + | * [[Measure space]] | ||
| + | * [[Measure Theory]] | ||
| + | * [[Measure Theory (subject)]] | ||
| + | * [[Template:Measure theory navbox]] | ||
| + | * [[Measures are monotonic and subtractive]] | ||
| + | * [[Min/max]] | ||
| + | * [[Monotonic set function]] | ||
| + | * [[Outer-measure]] | ||
| + | * [[P-system]] | ||
| + | * [[Positive and negative parts of a function]] | ||
| + | * [[Pre-image sigma-algebra]] | ||
| + | * [[Pre-image sigma-algebra/Definition]] | ||
| + | * [[Pre-image sigma-algebra/Proof of claim: it is a sigma-algebra]] | ||
| + | * [[Pre-measurable space]] | ||
| + | * [[Pre-measure]] | ||
| + | * [[Pre-measure space]] | ||
| + | * [[Pre-measure/Properties in common with measure]] | ||
| + | * [[Probability function]] | ||
| + | * [[Probability measure]] | ||
| + | * [[Probability space]] | ||
| + | * [[Random variable]] | ||
| + | * [[Real-valued function]] | ||
| + | * [[Ring generated by]] | ||
| + | * [[Ring of sets]] | ||
| + | * [[Set function]] | ||
| + | * [[Sigma-algebra]] | ||
| + | * [[Sigma-algebra generated by]] | ||
| + | * [[Sigma-ring]] | ||
| + | * [[Simple function (measure theory)]] | ||
| + | * [[Simple function (measure theory)/Definition]] | ||
| + | * [[Subtractive set function]] | ||
| + | * [[Trace sigma-algebra]] | ||
| + | * [[Types of set algebras]] | ||
Revision as of 00:35, 19 March 2016
- A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections
- A function is a measure iff it measures the empty set as 0, disjoint sets add, and it is continuous from below (with equiv. conditions)
- A map from two sigma-algebras, A and B, is measurable if and only if for some generator of B (call it G) we have the inverse image of S is in A for every S in G
- Additive function
- Algebra (Disambiguation)
- Algebra of sets
- Borel sigma-algebra
- Borel sigma-algebra generated by
- Class of sets closed under complements properties
- Class of sets closed under set-subtraction properties
- Class of smooth real-valued functions on R-n
- Class of smooth real-valued functions on R-n/Structure
- Classes of continuously differentiable functions
- Composition of measurable maps is measurable
- Conditions for a Dynkin system to be a sigma-algebra
- Conditions for a generated Dynkin system to be a sigma-algebra
- Conditions for a map to be a measurable map
- D-system
- Derivative
- Dynkin system
- Dynkin system generated by
- Dynkin system/Definition 1
- Dynkin system/Definition 2
- Dynkin system/Proof that definitions 1 and 2 are equivalent
- Extended real value
- Function terminology
- Generator
- Generator (sigma-algebra)
- Index of common sigma-algebras
- Integral
- Integral (measure theory)
- Integral of a positive function (measure theory)
- Integral of a positive function (measure theory)/Definition
- Integral of a simple function (measure theory)
- Integral of a simple function (measure theory)/Definition
- Lebesgue measure
- Limit of increasing sequence of sets
- Measurable function
- Measurable map
- Measurable space
- Measure
- Measure space
- Measure Theory
- Measure Theory (subject)
- Template:Measure theory navbox
- Measures are monotonic and subtractive
- Min/max
- Monotonic set function
- Outer-measure
- P-system
- Positive and negative parts of a function
- Pre-image sigma-algebra
- Pre-image sigma-algebra/Definition
- Pre-image sigma-algebra/Proof of claim: it is a sigma-algebra
- Pre-measurable space
- Pre-measure
- Pre-measure space
- Pre-measure/Properties in common with measure
- Probability function
- Probability measure
- Probability space
- Random variable
- Real-valued function
- Ring generated by
- Ring of sets
- Set function
- Sigma-algebra
- Sigma-algebra generated by
- Sigma-ring
- Simple function (measure theory)
- Simple function (measure theory)/Definition
- Subtractive set function
- Trace sigma-algebra
- Types of set algebras
