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International financial integration2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

edited by Sylvester C.W. Eijffinger and Jan J.G. Lemmen. 著
出版社：
ISBN：1840643838
出版时间：2003
标注页数：394页
文件大小：75MB
文件页数：404页
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图书目录

CHAPTER Ⅰ．SOME THEOREMS ON REAL-VALUED FUNCTIONS1

1．Sets and characteristic functions1

2．Neighborhoods，openness，closure5

3．Denumerable sets14

4．Functions and limits20

5．Bounds23

6．Upper and lower limits26

7．Semi-continuous functions38

8．Functions of bounded variation44

9．Absolutely continuous functions47

CHAPTER Ⅱ．THE LEBESGUE INTEGRAL52

10．Step-functions52

11．Riemann integrals57

12．U-functions and L-functions62

13．Integrals of U-functions and L-functions66

14．Upper and lower integrals72

15．The Lebesgue integral75

16．Consistency of Riemann and Lebesgue integrals85

17．Integrals over bounded sets89

18．Integrals over unbounded sets94

CHAPTER Ⅲ．MEASURABLE SETS AND MEASURABLE FUNCTIONS101

19．Arithmetic of measurable sets101

20．Exterior measure and interior measure109

21．Measurable functions118

22．Measurable functions and summable functions125

23．Equivalence of functions128

24．Summable products．Inequalities131

CHAPTER Ⅳ．THE INTEGRAL AS A FUNCTION OF SETS；CONVERGENCE THEOREMS136

25．Multiple integrals and iterated integrals136

26．Set functions150

27．The integral as a set function156

28．Modes of convergence160

29．Convergence theorems166

30．Metric spaces；spaces Lp177

CHAPTER Ⅴ．DIFFERENTIATION188

31．Dini derivates188

32．Derivates of monotonic functions194

33．Derivatives of indefinite Lebesgue integrals197

34．Derivatives of functions of bounded variation200

35．Derivatives of absolutely continuous functions207

36．Integration by parts209

37．Mean-value theorems209

38．Substitution theorems211

39．Differentiation under the integral sign216

CHAPTER Ⅵ．CONTINUITY PROPERTIES OF MEASURABLE FUNCTIONS218

40．The classes of Baire218

41．Metric density and approximate continuity222

42．Density of continuous functions in Lp．Riemann-Lebesgue theorem225

43．Lusin＇s theorem236

44．Non-measurable sets and non-measurable functions237

CHAPTER Ⅶ．THE LEBESGUE-STIELTJES INTEGRAL242

45．The difference-function242

46．Monotonic functions and functions of bounded variation248

47．Integrals and measure with respect to monotonic functions251

48．Examples255

49．Borel sets261

50．Dependence of integral on integrator264

51．Integrals with respect to functions of bounded variation269

52．Properties of the Lebesgue-Stieltjes integral271

53．Measure functions277

54．Measure functions and Lebesgue-Stieltjes measure287

55．Integrals with respect to a measure function295

56．Measure functions defined by integrals303

CHAPTER Ⅷ．THE PERRON INTEGRAL312

57．Definition of the Perron integral312

58．Elementary properties316

59．Relation to the Lebesgue integral322

60．Perron integral of a derivative323

61．Derivative of the indefinite Perron integral326

62．Summability of non-negative integrable functions328

63．Convergence theorems329

64．Substitution329

65．Integration by parts331

66．Second theorem of mean value335

CHAPTER Ⅸ．DIFFERENTIAL EQUATIONS336

67．Ascoli＇s theorem336

68．Existence and uniqueness of solutions338

69．The solutions as functions of parameters348

CHAPTER Ⅹ．DIFFERENTIATION OF MULTIPLE INTEGRALS366

70．Vitali＇s theorem366

71．Derivates of set functions372

72．Derivatives of indefinite integrals374

73．Derivatives of functions of bounded variation378

APPENDIX383

List of special symbols and abbreviations385

INDEX387