of the expression given in equation (10.21) is one, and it is 
possible to write AE(K + 2,K)/2 as the last expression in equa- 
waleyay. (AU@Saley)}q 
The power in 7 Ap (29,9) over the strip bounded by 
Hus HR» -"/2, and 7/2 is therefore given by 
at the point X49Vz when the sea surface is obServed as a function 
of time at that point. (Note E(u y,5,-7/2) and Eo(/ y,-7/2) are 
zero by definition.) 
For © fixed at 7/2, E,(p y17/2) is consequently connected 
with E(# ) as defined in Chapter 7. The Lebesgue Power Integral 
given by equation (10.22), evaluated as a function of time by 
any finite net (no matter how small), is by virtue of equation 
(10.19) indistinguishable from the result of evaluating the 
Lebesgue Power Integral given by equation (9.1) at a fixed point 
as a function of time. 
In addition, for all practical purposes, equation (10.23) 
and equation (10.24) determine the relationships between E,(p 58), 
E(w), [A(#)]°, and [a(n ,0)]°. 
Equations (10.23) and (10.24) are not strictly true. The 
functional relationships given do not hold exactly point for 
point. The relationships are true, however, in the sense that 
given that E,(“,©) is a continuous function with piecewise con- 
tinuous first partial derivatives, then E(#), and [A(p ye are 
point set functions with definite properties in a probability sense. 
To show this, consider the function E(#),* as yet not defined, 
and the function E(#) defined by (10.23). Also consider the 
DER: e 
