Lectures on Functional Analysis and the Lebesgue Integral

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    Lectures on Functional Analysis and the Lebesgue Integral

    This textbook,§based on three series of lectures held by the author at the University of§Strasbourg, presents functional analysis in a non-traditional way by§generalizing elementary theorems of plane geometry to spaces of arbitrary§dimension. This approach leads naturally to the basic notions and theorems.§Most results are illustrated by the small _ p spaces. The§Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes§Riesz, whose constructive definition of measurable functions leads to optimal,§clear-cut versions of the classical theorems of Fubini-Tonelli and§Radon-Nikodým.§§Lectures on§Functional Analysis and the Lebesgue Integral presents the most important topics for§students, with short, elegant proofs. The exposition style follows the§Hungarian mathematical tradition of Paul Erd_s and others. The order of the§first two parts, functional analysis and the Lebesgue integral, may be§reversed. In the third and final part they are combined to study various spaces§of continuous and integrable functions. Several beautiful, but almost§forgotten, classical theorems are also included.§§Both undergraduate§and graduate students in pure and applied mathematics, physics and engineering§will find this textbook useful. Only basic topological notions and results are§used and various simple but pertinent examples and exercises illustrate the§usefulness and optimality of most theorems. Many of these examples are new or difficult§to localize in the literature, and the original sources of most notions and§results are indicated to help the reader understand the genesis and development§of the field.§
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    Springer, Berlin
    ISBN / EAN
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