$L_{p}$ for $p==2$.

$L_{2}$ is by far the most important of $L_{p}$ because it is quantum mechanics states live, because the total probability of being in any state has to be 1!

$L_{2}$ has some crucially important properties that other $L_{p}$ don't (TODO confirm and make those more precise):

- it is the only $L_{p}$ that is Hilbert space because it is the only one where an inner product compatible with the metric can be defined:
- Fourier basis is complete for $L_{2}$, which is great for solving differential equation

- Lp space | 30, 408, 5
- Lebesgue integral of $L_{p}$ is complete but Riemann isn't | 91, 805, 11
- Lebesgue integral | 31, 1k, 15
- Calculus | 17, 7k, 159
- Mathematics | 17, 13k, 336
- Ciro Santilli's Homepage | 262, 182k, 3k

- Bra-ket notation | 472
- Carleson's theorem | 140
- Fourier inversion theorem | 41
- Fourier series | 143, 555, 8
- Function space | 11
- Hilbert space | 34, 184, 1
- $L_{2}$ | 130, 378, 3
- Lebesgue integral of $L_{p}$ is complete but Riemann isn't | 91, 805, 11
- Plancherel theorem | 150, 248, 2
- Riesz-Fischer theorem | 59, 306, 4
- Uncertainty principle | 292, 1k, 10