Editing Central limit theorem (section)

===Martingale difference CLT===
{{Main|Martingale central limit theorem}}
{{math theorem | math_statement = Let a [[Martingale (probability theory)|martingale]] <math display="inline">M_n</math> satisfy
* <math> \frac1n \sum_{k=1}^n \operatorname E\left[\left(M_k-M_{k-1}\right)^2 \mid M_1,\dots,M_{k-1}\right] \to 1 </math>  in probability as {{math|''n'' → ∞}},
* for every {{math|''ε'' > 0}}, <math> \frac1n \sum_{k=1}^n{\operatorname E\left[\left(M_k-M_{k-1} \right)^2\mathbf{1}\left[|M_k-M_{k-1}|>\varepsilon\sqrt{n}\right]\right]} \to 0 </math>  as {{math|''n'' → ∞}},

then <math display="inline">\frac{M_n}{\sqrt{n}}</math> converges in distribution to <math display="inline">\mathcal{N}(0, 1)</math> as <math display="inline">n \to \infty</math>.{{sfnp|Durrett|2004|loc=Sect. 7.7, Theorem 7.4}}{{sfnp|Billingsley|1995 |loc=Theorem 35.12}}}}