<![CDATA[Based on an interval system S in a locally compact metric space, we have a cell in a locally compact metric space, i.e. an interval compact in S. In addition, if a cell E and a function d : E ® R+ are given, we have proven the exsistence of Perron d ® fine partition on E. Using a Perron d ® fine partition on a cell E, we can contruct a Henstock integral of a real valued function in a locally metric space nondiscrete. By generalizing a range function of its function, i.e. from a set of all real numbers to a vector space, we can construct a Henstock integral of a vector valued function on a cell in locally metric space nondiscrete. This research used a method of literature study, which was done by examining relative integral theories, building new concepts and proving theorems using logical mathematic reasoning as well as right calculation.]]>
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