In particular, the only -space which is self-dual is .

While the use of functions is not as common as , they are very important in analysis and partial differential equations.

L spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces.

For , the space of -functions is a Banach space which is not a Hilbert space.The situation of having no linear functionals is highly undesirable for the purposes of doing analysis.Shia La Beouf takes his bike for a ride around town on Tuesday afternoon (August 8) in New York City.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.

For , the space of -functions is a Banach space which is not a Hilbert space.

The situation of having no linear functionals is highly undesirable for the purposes of doing analysis.

Shia La Beouf takes his bike for a ride around town on Tuesday afternoon (August 8) in New York City.

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.

And their performance together—one Ziegler likens to two animals in a cage—is a tour de force of both the physical and emotional variety.