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?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.