Note

Lebesgue's Criterion for Riemann Integrability

A rigorous topological proof of the sufficiency direction, using a compactness argument around the discontinuity set.

Summary

Criterion and mechanism

The note isolates the compactness and partition argument behind the sufficiency direction of the criterion.

Main result

The note proves the sufficiency direction: a bounded function on a compact interval is Riemann integrable when its discontinuity set has measure zero.

Contribution type
Expository reconstruction
Contribution
Topological proof of the sufficiency direction, organized around compact neighborhoods of the discontinuity set and finite partition control.
Mechanism
compactness, quarantining bad sets, finite partition
Format
PDF note