Actually, in the book:
Pugh, C. C. Real mathematical analysis. Second edition. Undergraduate Texts in Mathematics. Springer, Cham, 2015.
The Lebesgue integral is defined the way you suggested.
Actually, in the book:
Pugh, C. C. Real mathematical analysis. Second edition. Undergraduate Texts in Mathematics. Springer, Cham, 2015.
The Lebesgue integral is defined the way you suggested.