Mathematical Foundations · Real Analysis & Measure Theory

Mathematical Analysis and Measure Theory: L^p Spaces and Metric Structures in Probability

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Treatise on Analysis and Probability

Overview

Topics covered

  • Introduction
  • Spaces and Metric Structures: Mathematical Analysis and Measurement Theory
  • Measurement spaces and random variables
  • The Lebesgue integral and expected values
  • 2.1 Simple Functions
  • 2.2 Non-Negative Functions

Related concepts

Main connections

  • Calculus & differentiation
  • Measure theory & Lebesgue integration
  • Mathematical expectation & moments
  • Linear algebra & matrices
  • Conditional probability & independence
  • Variance & standard deviation

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

μ(⋃i=1∞Ai)=∑i=1∞μ(Ai)
View LaTeX source\mu\left(\bigcup_{i=1}^\infty A_i\right) = \sum_{i=1}^\infty \mu(A_i)