Henstock-Kurzweil integration on Euclidean spaces
著者
書誌事項
Henstock-Kurzweil integration on Euclidean spaces
（Series in real analysis, v. 12）
World Scientific, 2011
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内容説明・目次
内容説明
The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.
目次
- The One-Dimensional Henstock-Kurzweil Integral
- The Multiple Henstock-Kurzweil Integral
- Lebesgue Integrable Functions
- Further Properties of Henstock-Kurzweil Integrable Functions
- The Henstock Variational Measure
- Multipliers for the Henstock-Kurzweil Integral
- Some Selected Topics in Trigonometric Series
- Some Applications of the Henstock-Kurzweil Integral to Double Trigonometric Series.
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