=+There are many functions familiar from calculus that ought to be integrable but are of the types in the preceding problem and hence have infinite upper integral.

Examples are x-21( .= )(x) and x-1/2I(o. 1(x). Therefore, (15.10) is inappropriate as a definition of ffdu for nonnegative

f. The only problem with (15.10), however, is that it treats infinity the wrong way. To see this, and to focus on essentials, assume that u(2) <@ and that f is bounded, although not necessarily nonnegative or measur-

able F.