A Primer of Lebesgue Integration

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9780120839704: A Primer of Lebesgue Integration

The Lebesgue integral is the standard tool for mathematics, physics, or engineering. It is used where sequences or series arise and where one might wish to express the integral of a sum of integrals or vice versa. Itis essential in Fourier analysis and for the construction of Hilbert space and other function spaces. This primer gives a concrete treatment, building Lebesgue theory in a way parallel to the Riemann integral of beginning calculus. It makes the powerfultools of Lebesgue theory readily available to those in applied areas. It is a good introduction for those going on in mathematics as well as a refresher holding new insights for those in the field.
Professor Bear gives a clear and engaging account of this important and previously forbidding piece of mathematics, providing readers with a key to many areas of analysis.

*
* The Riemann-Darboux Integral
* The Riemann Integral as a Limit of Sums
* Lebesgue Measure on (0.1)
* Measurable-Sets - The Caratheodory Characterization

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From the Back Cover:

The Lebesgue integral is the standard tool for mathematics, physics, and engineering. It is used where sequences or series arise and where one might wish to express the integral of a sum as a sum of integrals or vice versa. It is essential in Fourier analysis and for the construction of Hilbert space. This primer gives a concrete treatment, building Lebesgue theory in a way parallel to the Riemann integral of beginning calculus. It makes the powerful tools of Lebesgue theory readily available to those in applied areas. It is a good introduction for those going on in mathematics and a refresher with new insights for those in the field. H.S. Bear gives a clear and engaging account of this important and previously forbidding piece of mathematics, providing readers with a key to many areas of analysis.

About the Author:

H.S. Bear is a professor at the University of Hawaii, Manoa and a member of both the American Mathematical Society and the Mathematical Association of America.

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