MathDB

8. Let

f

be a bounded real function defined on the unit cube

H

of the

n

-dimensional space and, for a given

y

, let

A_y

and

B_y

denote the parts of the interior of

H

on which

f>y

and

f<y

, respectively. Show that

f

is integrable in the Riemannian sense if and only if for every

y

almost all points of

A_y

and

B_y

are inner points. (R. 9)

Problem Statement