View source for Site projects:Measure theory plan

==Overview==
The plan is to stick pretty close to what Halmos does but introduce definitions found elsewhere, for example Measures, Integrals and Martingales introduces a ''pre-measure'' on an algebra of sets, and a ''measure'' on a {{sigma|algebra}} of sets. Halmos defines only measure and talks of wanting to extend it to a {{sigma|algebra}} but he defines these on a {{sigma|ring}} instead.

Inline with the [[Notes:Measure theory plan]] page we will use the terms and symbols which may be found on the bottom of this page.
==Questions / Problems / Reminders==
* A page (perhaps [[measure theory and sigma algebras notice]] will need to (have part of it) be transcluded onto each relevant page. Not sure on much more than this right now. It will have to:
** Urge the reader to keep algebras and sigma-algebras at the forefront of their minds when dealing with *measures
** Urge the reader to keep algebras and sigma-algebras at the forefront of their minds when considering the definition of measurable and measure spaces
==Progress==
{{:Site projects:Measure theory plan/Progress}}
==Symbols & Terms==
===Terms===
{| class="wikitable" border="1"
|-
! Term
! Meaning
! Comment
|-
! [[Pre-measure]] (positive)
| What it is now, but from a ring instead of algebra
|
|-
! [[Measure]] (positive)
| What it is now, but from  a {{sigma|ring}} instead of a {{sigma|algebra}}
|
|}
===Symbols===
{| class="wikitable" border="1"
|-
! Symbol
! Meaning
|-
! {{M|\mathcal{A} }}
| an ''algebra'' or {{sigma|''algebra''}} of sets.
|-
! {{M|\mathcal{B} }}
| Anything to do with Borel
|-
! {{M|\mathcal{C} }}
| an arbitrary collection of subsets of a set
|-
! {{M|\mathcal{G} }}
| Any generator of an object
|-
! {{M|\mathcal{R} }}
| a ''ring'' or {{sigma|ring}} of sets.
|-
! colspan="2" | Generated objects
|-
! {{M|\mathcal{B}(\cdot)}}
| Borel-sigma-algebra of a topological space
|-
! {{M|\sigma(\cdot)}}
| {{sigma|algebra}} generated by
|-
! {{M|\sigma_R(\cdot)}}
| {{sigma|ring}} generated by
|}
[[Category:Site projects]]