1．HISTORICAL INTRODUCTION 1
2．THE RIEMANN-COMPLETE INTEGRAL 13
3．VARIATIONAL PROPERTIES OF THE INTEGRAL 39
4．DIFFERENTIATION 74
5．LIMITS UNDER THE INTEGRAL SIGN 82
6．DOUBLE INTEGRALS AND FUBINI＇S THEOREM 100
7．THE CAUCHY AND DENJOY EXTENSIONS，AND THE INTEGRAL IN AN INFINITE RANGE 113
8．CONNECTIONS WITH EARLIER INTEGRALS 121
9．LINEAR TOPOLOGICAL SPACES，YOUNG＇S INEQUALITY AND INTEGRATION 127
10．INTEGRATION IN STATISTICS 148
References 162
Index 165