A primer of Lebesgue integration
著者
書誌事項
A primer of Lebesgue integration
Academic Press, c1995
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注記
Includes index
内容説明・目次
内容説明
The Lebesgue 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. It is 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 powerful tools 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. Features: * The Riemann-Darboux Integral * The Riemann Integral as a Limit of Sums * Lebesgue Measure on (0.1) * Measurable-Sets - The Caratheodory Characterization
目次
- The Riemann-Darboux integral
- the Riemann integral as a limit of sums
- Lebesgue measure on (0,1)
- measurable sets - the caratheodory characterization
- the Lebesgue integral for bounded functions
- properties of the integral
- the integral of unbounded functions
- differentiation and integration
- plane measure
- the relationship between mu and lambda
- general measures
- integration for general measures
- more integration
- the Radon-Nikodym theorem
- product measures
- the space L2.
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