POINT SETS AND PROPER INTEGRALS 
But the cells of may be subdivided, forming a new division A, 
which does not change the cells of so that Jq d = sg A , but so that 
com■ 
Then A contains complete sets (7, such that 
C> U-I-e, 
but no complete set such that 
Hence A contains complete sets (7, such that 
but no complete set such that 
From 2), 3), and 4), 5) we have 1), since e is arbitrarily small 
some constant k. 
com 
For suppose 
Let 
Then by 23 1 
in common wil 
or as > k, sr 
Let 
Then by 24, 
Thus 75. 
V^2 
Thus 3f 2 con 
point in comn 
Slj, 3i 2 , ••• cont? 
which is absur 
Corollary. 
This follows