Definition
A partition of an interval is a finite sequence of values xi such that
Each interval is called a subinterval of the partition. Let ƒ:→R be a bounded function, and let
be a partition of . Let
The upper Darboux sum of ƒ with respect to P is
The lower Darboux sum of ƒ with respect to P is
The upper Darboux integral of ƒ is
The lower Darboux integral of ƒ is
If Uƒ = Lƒ, then we say that ƒ is Darboux-integrable and set
the common value of the upper and lower Darboux integrals.
Read more about this topic: Darboux Integral
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