Cesari integral includes Henstock integral (Q1316440)

The author claims that the Henstock integral is included in the Burkill- Cesari integral [\textit{L. Cesari}, Trans. Am. Math. Soc. 102, 94-113 (1962; Zbl 0115.269); ibid. 114-146 (1962; Zbl 0115.270)]. More precisely, if \(f\) is Henstock integrable on \([a,b]\) then in the notations of Henstock we have \[ \liminf_{\mu(D)\to 0} (D)\Sigma f(\xi)(v- u)=\limsup_{\mu(D)\to 0}(D)\Sigma f(\xi)(v-u), \] where \(\mu(D)=\max\bigl\{| v-u|;\;[u,v]\in D\bigr\}\) and the divisions \(D\) are taken from a given family of \(\delta\)-fine divisions \(D=\bigl\{([u,v],\xi)\bigr\}\) with \(\xi= u\) or \(v\) for some \(\delta(\xi)>0\). For the Henstock integral see, for example, the reviewer [Lanzhou lectures on Henstock integration (1989; Zbl 0699.26004)].