Excerpt from The Theory of Functions of a Real Variable and the Theory of Fourier's Series, by E. W Hobson The foundations of the Integral Calculus, as based upon Riemann's definition of a definite integral, and its extensions, are discussed in Chapter V, where an account of the development of the subject from the point of View of Lebesgue's new definition of the definite Integral is also given. In later parts of the book I have introduced extensions of Lebesgue's definition, to the cases of improper integrals, taken over ...
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Excerpt from The Theory of Functions of a Real Variable and the Theory of Fourier's Series, by E. W Hobson The foundations of the Integral Calculus, as based upon Riemann's definition of a definite integral, and its extensions, are discussed in Chapter V, where an account of the development of the subject from the point of View of Lebesgue's new definition of the definite Integral is also given. In later parts of the book I have introduced extensions of Lebesgue's definition, to the cases of improper integrals, taken over finite or infinite domains, regarded as the limits of sequences of Lebesgue integrals. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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