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v • d • e 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). 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

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