This textbook leads the reader by easy stages through the essential parts of the theory of sets and theory of measure to the properties of the Lebesgue integral. The first part of the book gives a general introduction to functions of a real variable, measure, and integration, while the second part treats the problem of inverting the derivative of continuous functions, leading to the Denjoy integrals, and studies the derivates and approximate derivates of functions of a real variable on arbitrary linear sets. The author considers the presentation of this second part as the main purpose of his book.

Ralph L. Jeffery (1889-1975) was the head of the Mathematics Department at Queen's University for 18 years until his retirement in 1960.

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"Many interesting topics are treated in this book. Moreover, the presentation is very careful and readable."

Bulletin of the American Mathematical Society

"At times brings the reader close to the frontiers of knowledge in this field"

Scripta Mathematica

"There is about this book a refreshing air of personality. A reader brought up on other accounts of this theory, even written from the same point of view, will find many points of novelty."

Dalhousie Review