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Measure Theory
Overview of the basic and important objects studied in
measure theory
Set-structures
ring of sets
,
algebra of sets
,
[ilmath]\sigma[/ilmath]-ring
,
[ilmath]\sigma[/ilmath]-algebra
,
hereditary [ilmath]\sigma[/ilmath]-ring
measurable space
Measures
Pre-measure
[ilmath]\leadsto[/ilmath]
outer-measure
[ilmath]\leadsto[/ilmath]
measure
(see
Extending pre-measures to measures
(via:
Extending pre-measures to outer-measures
[ilmath]\rightarrow[/ilmath] "Restricting outer-measures to measures" maybe?). Alternatively:
inner-measure
can be used.
measure space
Functions
measurable map
,
simple function
(
standard representation
)
Spaces
Integrals
Integrating a simple function
[ilmath]\leadsto[/ilmath]
Integral of a positive function
[ilmath]\leadsto[/ilmath]
Integrating all measurable functions
Todo (Navbox project): Fill this in
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Measure Theory
Todo: Navbox project
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