$L_{p}$ 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

- $L_{p}$ | 30, 156, 1
- Lebesgue integral of $L_{p}$ is complete but Riemann isn't | 89, 547, 7
- Lebesgue integral | 23, 843, 12
- Calculus | 11, 4k, 96
- Mathematics | 17, 10k, 239
- Ciro Santilli's Homepage | 238, 147k, 2k

- Carleson's theorem | 140
- Fourier inversion theorem | 41
- Fourier series | 132, 378, 8
- Hilbert space | 34
- $L_{2}$ | 126
- Lebesgue integral of $L_{p}$ is complete but Riemann isn't | 89, 547, 7
- Riesz-Fischer theorem | 59, 302, 4
- Uncertainty principle | 263, 528, 8