README.md

HOL's Probability Theory

This directory contains HOL4's Measure, Lebesgue integral and Probability theories.

Preliminaries

 extrealScript.sml            * The theory of extended reals
 real_topologyScript.sml      * Elementary Topology in Euclidean Space (from HOL Light)
 derivativeScript.sml         * Univariate Derivative Theory in R^1 (from HOL Light)
 integrationScript.sml        * Henstock-Kurzweil (gauge) Integral (from HOL Light)

Measure, Integral and Probability Theory defined on extended reals

 sigma_algebraScript.sml      * Sigma-algebra and other system of sets
 measureScript.sml            * Measure Theory defined on extended reals 
 real_borelScript.sml         * Borel-measurable sets generated from reals 
 borelScript.sml              * Borel sets and Borel measurable functions
 lebesgueScript.sml           * Lebesgue integration theory
 martingaleScript.sml         * Martingales based on σ-finite filtered measure space
 probabilityScript.sml        * Probability Theory based on extended reals

Measure, Integral and Probability Theory defined on reals

 real_measureScript.sml       * Measure Theory defined on reals
 real_lebesgueScript.sml      * Lebesgue integrals based on reals
 real_probabilityScript.sml   * Probability Theory based on reals

Utilities

 hurdUtils.{sml|sig}          * Some useful tools originally defined by Joe Hurd
 util_probScript.sml          * Utility lemmas needed by other scripts
 iterateScript.sml            * Generic iterated operations and special cases of sums over N and R
 productScript.sml            * Products of natural numbers and real numbers