Repeated Integration

We shall use the following notation. Let x= (x1, . . ., xn) be a point of an n-dimensional interval I1,

I1 = {x = (x1, . . . , xn) : ai ≤ xi ≤ bi, i = 1, . . . ,n} ,

and let y be a point of an m-dimensional interval I2,

I2 = {

y = (y1, . . . , ym )

: cj ≤ yj ≤ dj, j = 1, . . . ,m }

.