Kaczor W.J. — Problems in Mathematical Analysis III: Integration :: Электронная библиотека попечительского совета мехмата МГУ

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Kaczor W.J. — Problems in Mathematical Analysis III: Integration

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Название: Problems in Mathematical Analysis III: Integration

Автор: Kaczor W.J.

Аннотация:

A supplement to undergraduate and undergraduate textbooks in mathematical analysis. The third volume in the series focuses on the Riemann-Stieltjes integral and the Lebesgue integral for real functions of one real variable. The first half contains the problems, and the second the solutions and explanations

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 368

Добавлена в каталог: 09.04.2008

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Предметный указатель

Abel test for convergence of improper integrals      33
Absolutely continuous function      77
Almost everywhere      65
Approximation theorem for measurable functions      65
Arzela theorem      20
Banach indicatrix      78
Banach — Zarecki theorem      78
Bernstein theorem      87
Bessel’s inequality      86
Bonnet form of second mean value theorem      18
Cantor function      66
Caratheodory condition      57
Cauchy theorem      31
Cesaro mean of the Fourier series      88
Change of variable formula      15
Change of variable formula for Lebesgue integrals      79
Chcbyshev inequality      44
Convergence in measure      68
Dini — Lipschitz test for convergence of Fourier series      84
Dirichlet test for convergence of improper integrals      33
Dirichlet — Jordan test for convergence of Fourier series      84
Duplication formula      41
Egorov theorem      67
Elementary set      52
Equi-integrable functions      74
Essential supremum      70
Essentially bounded function      70
Euler’s beta function      41
Euler’s gamma function      35
Fatou lemma for Riemann integrals      20
Fatou theorem      60
Fejer kernel      334
Fejer theorem      89
Fejer — Lebesgue theorem      89
First mean value theorem      9
Fourier coefficients      62
Fourier series      82
Frechet theorem      69
Fresnel’s integrals      39
Function, Lebesgue measurable      64
Function, of bounded variation      10
Function, of negative variation      10
Function, of positive variation      10
Function, simple      65

Function, singular      80
Helly theorem      18
Holder condition      12
Holder inequality      46
Holly selection theorem      18
Integration by parts for Lebesgue integrals and absolutely continuous functions      80
Jensen inequality      47
Jensen inequality for Lebesgue integral      76
Lebesgue constants      88
Lebesgue criterion for Riemann integrability      64
Lebesgue inner measure      59
Lebesgue point      80
Lebesgue theorem      69
Lipschit z condition of order a      12
Lipschitz condition      114
Lipschitz constant      114
Lusin theorem      68
mesh      3
Minkowski inequality      48
Monotone convergence theorem for the Riemann integral      20
Opial inequality      51
Pairwise separate sets      52
Parseval formula      325
Partial integration formula      15
Point of approximate continuity      81
Point of density      62
Point of dispersion      62
Point of outer density      81
Point of outer dispersion      81
Riesz theorem      69
Saltus function      14
Schwarz inequality      42
Second mean value theorem      18
Separate intervals      52
Steffensen inequality      49
Step function      6
Stirling formula      42
Total variation      10
Translate of a function by t      76
Uniform convergence of an improper integral      35
Vitali theorem      69
Vltali set      63
Wiener thoorem      90
Young inequality      45

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