Sigma-Algebras as the Domain for Measurable Sets
Abide by Reason introduces sigma-algebras for learners who are comfortable with sets and power sets but have not yet seen how measure theorists restrict which subsets are allowed to have “size.”
Measurable Spaces, Measures, and Measure Spaces: The Basic Triple
This note is for learners sorting out the terminology jungle around “measurable spaces,” “measure spaces,” and “measurable sets.”
Measure as Countably Additive Set Function on a Measurable Space
Abide by Reason precisely defines what a measure is for viewers who have seen examples like length and probability but not the general axioms.
Examples of Sigma-Algebras and Measurable vs Non-Measurable Subsets
This note serves viewers who need concrete finite examples to internalize the abstract definition of sigma-algebras and measurability.
Dirac Measure as Point Mass and Connection to Dirac Delta
Abide by Reason uses the Dirac measure example for students familiar with physics’ Dirac delta but new to its rigorous measure-theoretic interpretation.