f {\displaystyle f} and g {\displaystyle g} are square integrable functions, f ( x ) ¯ {\displaystyle {\overline {f(x)}}} is the complex conjugate of f ( x ) {\displaystyle f(x)} , A {\displaystyle A} is the set over which one integrates—in the first definition (given in the introduction above), A {\displaystyle A} is ( − ∞ , + ∞ ) {\displaystyle (-\infty ,+\infty )} ; in the second, A {\displaystyle A} is [ a , b ] {\displaystyle [a,b]} .