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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Lectures on Functional Analysis and the Lebesgue Integral (Paperback, 1st ed. 2016)
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Lectures on Functional Analysis and the Lebesgue Integral (Paperback, 1st ed. 2016)
Series: Universitext
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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-Nikodym. 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 Erdos 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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