I'm currently trying to figure out the following inequality. It looks like an inequality for the exponential sum, but I can't verify it or find a source explaining it any further. Most likely it has to do with the remainder I guess... $$|E[\exp(itX_{n,k})|F_{n,k-1}]-1-\frac{1}{2}t^2E[X_{n,k}^2|F_{n,k-1}]|\\ \leq \frac{1}{6}|t|^3E[|X_{n,k}|^3\mathrm{1}_{|X_{n,k}|\leq \epsilon}\big{|}F_{n,k-1}]+t^2E[X_{n,k}^21_{X_{n,k}>\epsilon}|F_{n,k-1}]$$

Where $E[X_{n,k}|F_{n,k-1}]=0$ for all $k,n \in \mathbb{N}$

Especially this is taken from Dvoretzky, 1972, ASYMPTOTIC NORMALITY FOR SUMS OF DEPENDENT RANDOM VARIABLES and can be found in the proof of theorem 2.1 equality (4.4). Thanks in advance.