function face yIe*, as yet not defined, and the function race ne 
defined by equation (10.24). E(y) is assumed to have a piecewise 
continuous partial derivative with respect to#. Forma net over 
the # axis. Also find fac uiiles For each net interval, H 5,45 to 
Mon, take the value of [AGHe ae ie. Pick a number from a Gaussian 
distribution with a zero mean anc unit standard deviation and 
multiply [A( 5,41) ]° by its square. Assign the result to the 
entire net interval, M5,.59Hon: The resulting new function is 
piecewise continuous, and as, say, a function of w* it can be 
integrated from 0 to # to find a new cumulative power distribution. 
The new cumulative power distribution will be continuous, since 
the integral of a piecewise continuous function is continuous. 
Now consider the class of all possible functions which would 
result from this operation as the mesh of the net approaches zero. 
There are an infinite number. Define the function, [ace )1°*, 
mentioned above, to be one of the functions; and define the 
function E(p)* to be the integral of [aC )]o*. 
How does [A()]** differ from [A(#)]°? First of all it is 
continuous no where. Each point value of [aCm)]°* can differ from 
the value at any nearby point by any amount. The function, 
[aC w)1**, cannot be graphed, but it can be visualized as a cloud 
of points scattered above, below, and on the graph of [a(u )]° 
such that no point is above any other point and there is a point 
for every point of WOT kee In addition, if a new net is taken 
over face )1e*, the Lebesgue integral from M5, to 5,45 of this 
function has the same value as the integral from eon to mw On+2 
of EA@ee vies This statement can be proved by methods similar to 
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