23/03/18 23:56:11.13 M09HE8oG.net
>>545
つづき
URLﾘﾝｸ(en.wikipedia.org)
For the sequence space ｌp, see Sequence space § ｌp spaces.
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910).
Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces.
Hilbert spaces
See also: Square-integrable function
Hilbert spaces are central to many applications, from quantum mechanics to stochastic calculus. The spaces
L^2 and l^2 are both Hilbert spaces. In fact, by choosing a Hilbert basis
E, i.e., a maximal orthonormal subset of
L^2 or any Hilbert space, one sees that every Hilbert space is isometrically isomorphic to
l ^2(E) (same E as above), i.e., a Hilbert space of type ｌ2.
URLﾘﾝｸ(ja.wikipedia.org)
Lp空間
可算無限次元における p-ノルム
詳細は「数列空間」を参照
l^2二乗総和可能な数列の空間で、ヒルベルト空間でもある；
(引用終り)
以上