The conditions on W(#) are that W(#) be between O and 
2r and that its value be random and equally probable for any 
particular #. Equation (7.28) states this condition in sta- 
tistical terms. The equation is read, "The probability that 
VCH one) is less than a27 equals a," where a lies between 
zero and one. Such a condition is equivalent to the statement 
that the phases are independent (Tukey and Hamming [1949]). 
The integral can then be thought of as the limit of a se=- 
quence of sums such as equation (7.7) in which the ¥ (#5, ,,) 
are chosen from a table of random numbers. Of course each time 
the process is carried out, the sum will be different because 
the phases are different. In addition, it is not possible to 
write down an expression for the result of the passage to the 
limit. 
The function, W(), as defined by equation (7.28) is a 
point set function. It cannot be graphed. It is continuous no 
where. For a particular net over the axis, and after the choices 
from a table of random numbers have been made, it is a definite 
function. 
Now consider all possible point set function, (#), which 
could be chosen by the probability law which has been given. 
And consider all the corresponding 7 (t) which could be deter- 
mined from ¥(m) once E(#) is fixed. In the limit, a whole 
statistical class of functions 7 (t) would be the result. What 
properties would they have in common? And if a part of one of 
these functions from this statistical class is given, how can 
E(y) be found? 
~ 136 - 
