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As in the case of an L2-space, an -function is really an equivalence class of functions which agree almost everywhere.
It is possible for a sequence of functions to converge in but not in for some other , e.g., converges in but not .
However, if a sequence converges in and in , then its limit must be the same in both spaces.
An integral instead of a sum is used to define the are sometimes called quadratically integrable functions, square-integrable functions or square-summable functions, but sometimes these terms are reserved for functions that are square-integrable in some other sense, such as in the sense of a Riemann integral (Titchmarsh 1976).
If we use complex-valued functions, the space except in some trivial cases.