Loya P. Lebesgue's Remarkable Theory of Measure and Integration with Prob. 2006

Textbook in PDF format

A course on Lebesgue's Theory of Measure and Integration.
Prologue: The paper that changed integration theory... forever
Some remarks on Lebesgue’s paper
Finite additivity
Measure & probability: finite additivity
Finitely additive integration
Countable additivity
Measure and probability: countable additivity
Reactions to the Extension & Regularity Theorems
Integration
Basics of Integration Theory
Some applications of integration
Further results in measure and integration
Fubini's theorem and Change of Variables
Bibliography