point at (27 6/50,sin7/1/5). An area element from the net which 
covers this point gives no contribution since 
(2 - 7/4 - 7/4 + 3/2) = 0. Also note that 7 (x,y,0) for a fixed 
yl/2 
y is an almost periodic function in x since (24/25 is an 
irrational number. 
The Gaussian case of the Lebesgue Power Integral for short crested 
wave systems 
By the techniques employed above, many strange and wonderful 
sea surfaces can be created. It appears that none of them would 
be quite as strange and wonderful and realistic as the one which 
will now be described. The short crested wave system given by 
the Gaussian case of the Lebesgue Stieltjes Power Integral appears 
to describe the actual surface of the sea in the best possible 
way within the limits of the linearization assumptions of Chapter 2. 
The Gaussian case can be obtained in the following way. Equ- 
ations (9.2) through (9.13) are still imposed. In addition, if 
a small circle of radius 6 is placed around any point, say, 
CH 4305), then it is required that the absolute value of the dif- 
ference between E>(# 4) at the point and at any other point in 
the circle be smaller than an epsilon (which may depend on delta). 
Stated another way, E,(y ,®) is a continuous function in both 
variables, and it is monotonic non-decreasing in both variables 
(see Courant, Vol. I). Equations (9.41) and (9.42) are another 
way to impose these conditions. Finally, ¥(#,e) must have a 
value between zero and 27, and its value is picked by the proba- 
bility law given in equations (9.44) and (9.45). 
If equations (9.2) through (9.13) hold, and if the conditions 
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