One version of this property uses the existence of the Cousin's lemma's guaranteed delta-fine sets where delta is a gauge function.
One version of this property uses the existence of the Cousin's lemma's guaranteed delta-fine sets where delta is a gauge function. That variant is named for Henstock and Kurzweil. Given a set, determining if a function has another version of this property involves sets that are non-empty, closed under complementation, and closed under countable unions of elements. Those (*) sigma-algebra sets have subsets that are measurable. Another form of this property uses refinements of partitions to find that the supremum of the infimum and the infimum of the supremum of certain sums are equal. Forms of this are named Darboux, Lebesgue, and Riemann. For 10 points, name this property that, by the Fundamental Theorem of Calculus, means a continuous function must have an antiderivative.
One version of this property uses the existence of the Cousin's lemma's guaranteed delta-fine sets where delta is a gauge function.
integrable [accept Riemann integrable; accept Lebesgue integrable; accept Henstock-Kurzweil integrable; accept Denjoy integrable; accept Peron integrable; accept gauge integrable; there are probably a lot more too, so prompt on other types of being integrable; accept any word forms such as integrating or being able to take the integral, etc]