139 
that ae v;=0 and that the inequality MOR follows from 
Dis SOE 
In this case 
26 .l 
IJ 26 4 
| NE, 
fre dé Tig ES log 
; 5 gj 5 q 
q 
me 
If therefore u indicates the greatest value of 7 for which 6; ‚8 —1 <1 
we have according to (5) and (6) 
EN A vu 
nen (Giang Steak Le BR eli 
5 q j=l 
E 
because f(6;-1§—1) and f(A; §—1) are zero for 7 > wu owing to 
E>. The aforesaid inequality holds for any measurable set Z to 
the right of 3 which has no point in common with any of the 
productions of the segments (dj, dj ;). We shall now assume that 
this set / lies to the left of a point y and that for any point § of 
E the inequality F(&2q holds good. In this case the left-hand 
member of (7) is not less than Ka multiplied by the measure of Á. 
x 
Now we can choose y so close to the origin that the measure of 
the subset between 0 and y of the productions is < 3qy. The set 
between O and y of the points § for which F'(§) 2 g, has therefore 
a measure less than 
2 4 u 
3qy + 8 + measure F< 3gy + B+ A log = v;(A;—0;-i) - (8) 
DEL 
For q <4 the right-hand member is less than 6qy, if y lies close 
enough to the origin and 2 is chosen properly. With a view to this 
we assume 3—=gqy; if y lies close enough to the origin, u is so 
great that for any j > u 
q 
oa 
4 log — 
q 
In this case we can therefore define an integer number w Su in- 
dependent of y, so that this inequality holds good for any j > w. 
Finally we choose y so close to the origin that 
Apt aN OM 
SS = vj (0; Et 0j—) <a q 
q q j=l 
