A systematic approach on some relevant theorems that follows from Kolmogorov's axioms

TL;DR

This paper systematically presents key theorems in probability theory derived from Kolmogorov's axioms, set theory, and inference rules, providing a self-contained resource for students before advancing to complex topics.

Contribution

It offers a structured, comprehensive compilation and proof of fundamental probability theorems directly stemming from foundational axioms and set theory, tailored for educational purposes.

Findings

Key theorems are systematically listed and proven.

Provides a self-contained educational resource.

Lays groundwork for advanced probability studies.

Abstract

A selection of the relevant theorems of Probability Theory that comes directly from Kolmogorov's axioms, Set Theory basic results, definitions and rules of inference are listed and proven in a systematic approach, aiming the student who seeks a self-contained account on the matter before moving to more advanced material.