A function y(x) is said to be square integrable if
∫−∞∞∣f(x)∣2dx<∞
for linear space:
(f+g)(x)=f(x)+g(x)
f(ax)=af(x)
for the space L[a,b] of all square integrable functions:
if
∫−∞∞∣(f+g)(x)∣2dx<∞
then
∫−∞∞∣f(x)∣2dx+∫−∞∞∣g(x)∣2dx<∞
∫f(ax)dx=a∫f(x)dx
so, this is a linear space over a vector field R
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