eral was defined by a net over the # ,© plane as the mesh of 
the net was shrunk to zero. Consider the two values of / given 
by Hx and # y,5 in the net defined by equation (9.14), and break 
up this small increment, Ap , into N much smaller increments as 
shown by equation (10.5). The relations between the me iods ji is 
involved are given by equation (10.6). Also consider a full net 
over © from -1/2 to 7/2, for each of the smaller nets given in 
equation (10.5). The values of 96 at the net points will also 
need to depend on the particular net interval, uv 2k+2j to 
P oto 5429 and they are therefore designated by subscripts like 
°1; as shown by equation (10.8). 
One property that these Lebesgue Power Integrals have (and 
which has not been proved in this paper) is that they are the same 
as the ordinary Riemann integral in that it is possible to break 
up the area of integration into small touching but non-overlapping 
pieces and the total integral is the sum of the integrals over 
the smaller pieces. Consequently, the contribution to the total 
disturbance created by the power in the semicircular strip from 
Py» to My, and from -1/2 to 7/2 is given by the limit of the 
partial sum given by equation (10.9).* NA p(X st) is thus 
the contribution of this strip to the total integral as observed 
at the fixed point X493° The proof of equation (10.3) consists 
essentially of picking an appropriate sub-net in this semicurcular 
striv to obtain the desired properties. 
In equation (10.10), it is pointed out that for any 
*Note that the R here has nothing to do with the R of Chapter 
9. it is just an integer. 
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