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{wiki=Khintchine_inequality}

For independent Rademacher signs $\varepsilon_n$, every $0<p<\infty$ admits constants $A_p,B_p>0$ such that
$$
A_p\left(\sum_n|a_n|^2\right)^{1/2}
\leq\left(\mathbb E\left|\sum_n\varepsilon_na_n\right|^p\right)^{1/p}
\leq B_p\left(\sum_n|a_n|^2\right)^{1/2}.
$$

Khintchine inequality

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 163 / 1 / a / Solution

{wiki=Khintchine_inequality}

The Khintchine inequality is a result in mathematical analysis, particularly in the study of probability theory and functional analysis. It pertains to the properties of sums of independent random variables, specifically regarding their expected values and moments.


Khintchine inequality

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Khintchine inequality

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