ABSTRACT
Two facets of this statement deserve attention. First, the result (ii) includes (i). Secondly, if the integral (4.01) converges absolutely, then necessarily it converges
uniformly; on the other hand, it is readily verified by partial integration that the integral
ff$dt ( 0 < 6 < I), (4.02)
for example, converges uniformly at both limits for x 2 X (>0), but does not converge absolutely at the upper limit.'
