Basic real analysis, by Houshang H. Sohrab, section 7.3, Sets of Measure Zero and Lebesgue’s Integrability Condition, pp. 264–271
jstor.org
Brown, A. B. (1936-09). “A Proof of the Lebesgue Condition for Riemann Integrability”. The American Mathematical Monthly43 (7): 396–398. ISSN0002-9890. JSTOR2301737.
Introduction to Real Analysis(PDF) , updated April 2010, William F. Trench, 3.5 "A More Advanced Look at the Existence of the Proper Riemann Integral", pp. 171–177
unapologetic.wordpress.com
Lebesgue’s Condition, John Armstrong, December 15, 2009, The Unapologetic Mathematician
Brown, A. B. (1936-09). “A Proof of the Lebesgue Condition for Riemann Integrability”. The American Mathematical Monthly43 (7): 396–398. ISSN0002-9890. JSTOR2301737.