mds/measures.qmd at main · Morrison-Lab/mds · GitHub

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---
title: "Measures"
format:
  html: default
  revealjs:
    output-file: measures-slides.html
  pdf:
    output-file: measures-handout.pdf
  docx:
    output-file: measures.docx
---

{{< include mds/_measures.qmd >}}

## Further reading {#sec-further-reading}

- @billingsley1995probability
  develops measure theory and builds probability on it.
  Its early chapters define $\sigma$-algebras, measures, and their basic properties.
- @folland1999real
  is a graduate text on measure and integration;
  its first chapters treat $\sigma$-algebras and measures.
- @gut2013
  is a graduate course in probability
  that opens with a chapter on introductory measure theory.

-   @wikipedia_sigma_algebra --- $\sigma$-algebras and their generators

-   @wikipedia_closure_mathematics --- closure under an operation

-   @wikipedia_borel_set --- Borel sets

-   @wikipedia_disjoint_sets --- disjoint sets

-   @wikipedia_series_mathematics --- series and partial sums

-   @wikipedia_monotone_convergence_theorem --- the monotone convergence theorem

-   @wikipedia_sigma_additive_set_function --- additive and $\sigma$-additive set functions

-   @wikipedia_measure_mathematics --- measures, with examples

-   @wikipedia_counting_measure --- counting measure

-   @wikipedia_measurable_space --- measurable spaces

-   @wikipedia_lebesgue_measure --- Lebesgue measure and its construction

-   @wikipedia_null_set --- null sets

-   @wikipedia_almost_everywhere --- properties that hold almost everywhere

-   @wikipedia_finite_measure --- finite measures

-   @wikipedia_sigma_finite_measure --- $\sigma$-finite measures

-   @wikipedia_probability_measure --- probability measures

-   @wikipedia_probability_space --- probability spaces

-   @wikipedia_sample_space --- sample spaces

-   @wikipedia_event_probability_theory --- events

-   @wikipedia_outcome_probability --- outcomes

-   @wikipedia_measurable_function --- measurable functions

-   @wikipedia_lebesgue_integration --- the Lebesgue integral

## References {.unnumbered}

::: {#refs}
:::