Difference between revisions of "Site projects:Patrolling measure theory/Task list"

Revision as of 02:01, 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) Work required
• Algebra of sets Work required
• 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 Work required
• 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 DONE Alec (talk) 01:54, 19 March 2016 (UTC)
• Derivative
• Dynkin system DONE Alec (talk) 01:54, 19 March 2016 (UTC)
• Dynkin system generated by Work required
• Dynkin system/Definition 1 DONE Alec (talk) 01:54, 19 March 2016 (UTC)
• Dynkin system/Definition 2 DONE Alec (talk) 01:54, 19 March 2016 (UTC)
• Dynkin system/Proof that definitions 1 and 2 are equivalent DONE Alec (talk) 01:54, 19 March 2016 (UTC)
• Extended real value
• Function terminology
• Generator Work required
• Generator (sigma-algebra) DONE Alec (talk) 01:58, 19 March 2016 (UTC)
• Index of common sigma-algebras
• Integral DONE Alec (talk) 02:01, 19 March 2016 (UTC)
• Integral (measure theory) DONE Alec (talk) 02:01, 19 March 2016 (UTC)
• Integral of a positive function (measure theory) Work required
• Integral of a positive function (measure theory)/Definition Work required
• Integral of a simple function (measure theory) DONE Alec (talk) 02:01, 19 March 2016 (UTC)
• Integral of a simple function (measure theory)/Definition DONE Alec (talk) 02:01, 19 March 2016 (UTC)
• Lebesgue measure
• Limit of increasing sequence of sets
• Measurable function DONE Alec (talk) 01:58, 19 March 2016 (UTC)
• Measurable map LOCK
• Measurable space
• Measure LOCK
• Measure space
• Measure Theory
• Measure Theory (subject)
• Template:Measure theory navbox Work required
• Measures are monotonic and subtractive
• Min/max
• Monotonic set function
• Outer-measure
• P-system DONE Alec (talk) 01:58, 19 March 2016 (UTC)
• Positive and negative parts of a function
• Pre-image sigma-algebra DONE Alec (talk) 00:42, 19 March 2016 (UTC)
• Pre-image sigma-algebra/Definition DONE Alec (talk) 00:42, 19 March 2016 (UTC)
• Pre-image sigma-algebra/Proof of claim: it is a sigma-algebra DONE Alec (talk) 00:42, 19 March 2016 (UTC)
• 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 DONE Alec (talk) 01:49, 19 March 2016 (UTC)
• Sigma-algebra generated by Marked as dire
• Sigma-ring LOCK
• Simple function (measure theory) LOCK
• Simple function (measure theory)/Definition LOCK
• Subtractive set function
• Trace sigma-algebra DONE Alec (talk) 00:58, 19 March 2016 (UTC)
• Types of set algebras