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I understand the definition of Henstock integrable function on $[a, b]$, i.e.,

$f$ is Henstock-Kurzweil integrable on $[a, b]$ if there is $A \in \mathbb{R}$ with property for every $\varepsilon>0$ there is a gauge $\delta$ such that for any $\delta$-fine division $D=\{(t,[u,v])\}$ we have $$(D)\sum|f(t)(v-u)-A|< \varepsilon.$$

I haven't seen a definition of the Henstock integrable function on $D$ when $D$ is anything other than an interval. Is there a general form for the integral over $D$? How to define division?

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