Hence the result of the integration will be the reciprocal of the normalizing function.
2.
If is not normalized, then dividing by its norm gives the normalized function ? } }.
3.
The idea is that dividing the function by appropriate normalizing functions, and looking at the limiting behavior of the result, can tell us much about the limiting behavior of the original function itself.
4.
Specifically it says that the normalizing function } }, intermediate in size between of the law of large numbers and } } of the central limit theorem, provides a non-trivial limiting behavior.
5.
Finally, the last term is the inner product of two normalized functions that are at an angle of " & omega; ij " to each other, which gives cos " & omega; ij " by definition.
6.
The last line follows from the previous one by recognizing that the function inside the integral is the density function of a random variable distributed as G ( \ boldsymbol { \ eta } | \ boldsymbol { \ chi } + \ mathbf { T } ( x ), \ nu + 1 ), excluding the normalizing function f ( \ dots ) \,.
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