Topic: Simple Functions and Approximation

Worked Approximations for Indicators and Step Profiles

Why Egorov Requires Finite Measure

Truncation Before Quantization for Unbounded Functions

Sums, Products, Maxima, and Minima of Simple Functions

Simple Functions as Finite-Valued Measurable Maps

Range Quantization for Bounded Measurable Functions

Proof of Monotone Simple Approximation

Proof of Lusin’s Theorem by Simple Approximation

Proof of Egorov’s Theorem by Exceptional Sets

Lusin’s Theorem on Finite-Measure Subsets of the Real Line