Topic: Simple Functions and Approximation

Lusin Approximation for Unbounded Measurable Functions

Lusin’s Theorem for Indicator Functions

Level Sets and Disjoint Forms of Simple Functions

Error Bounds from Quantization and Truncation

Dyadic Simple Approximants for Nonnegative Functions

Egorov’s Theorem on Finite-Measure Spaces

Common Errors in Simple-Function Approximation

Choosing Egorov Sets with Prescribed Error