143 
increasing, series of integrals is limited. Now let s; be the integral 
(C) of f.(§) and s=lims,. The function Si(—f,(§) is either always 
2 or always <0 and integrable (C), hence according to proposition 
3 it is summable with s;—s, for sum. As the monotone series $:—S, 
has s—s, for limit, /($)—/,(§) is summable with s—s, for sum. 
From this it ensues that /(§)—/,(&) is integrable (C) with s—s, for 
integral, so that /(§) is integrable (C) with s for integral. 
