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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