Theorem 1.1 (Khinchin’s inequality). Assuming that:

• ${\{{𝜀}_n\}}_{n=1}^N$ be IID random variables with $\mathbb{P}({𝜀}_n=1)=\mathbb{P}({𝜀}_n=-1)=\frac{1}{2}$

• $1<p<\infty$

• $x_1,\dots ,x_N\in ℂ$

Then