Some comments on the McShane and Henstock integrals (Q1978872)

The main result (among others) is: A function \(f:[a,b] \to \mathbb R\) is McShane integrable on \([a,b]\) if and only if there is a number \(L\) with the following property: for each \(\varepsilon >0\) there exists a gauge \(\delta \) on \([a,b]\) such that \(|\sum f(x_i) \mu (E_i) - L |< \varepsilon \) whenever \(\{(x_i,E_i): 1\leq i\leq n\}\) is a \(\delta \)-fine tagged measurable partition of \([a,b]\). By \(\mu \) the Lebesgue measure is denoted, \(E_i\) are measurable sets with \(\bigcup E_i =[a,b]\), \(x_i \in E_i\) for \(1\leq i\leq n\).