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Mathematical Foundations · Real Analysis & Measure Theory

Mathematical Analysis and Theory of Measure · Absolute Continuity and Radon-Nikodym Theorem

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Mathematical Analysis & Measurement Theory

Overview

Topics covered

  • Introduction
  • Absolute continuity and the Radon-Nikodym Theorem
  • Signed measures and Hahn and Jordan decompositions
  • Positive, negative and null sets
  • Absolute continuity and singularity: Definitions and characterization epsilon-delta
  • The Radon-Nikodym Theorem

Related concepts

Main connections

  • Calculus & differentiation
  • Measure theory & Lebesgue integration
  • Maximum likelihood estimation
  • Hypothesis testing
  • Variance & standard deviation
  • Normal (Gaussian) distribution

Compatible notation

Mathematical sample in LaTeX

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

ν(⋃n=1∞En)=∑n=1∞ν(En).
View LaTeX source\nu\Big(\bigcup_{n=1}^\infty E_n\Big) = \sum_{n=1}^\infty \nu(E_n).