Displaying similar documents to “Another Perron type integration in n dimensions as an extension of integration of stepfunctions”

Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion

Tuo-Yeong Lee (2005)

Mathematica Bohemica

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It is shown that a Banach-valued Henstock-Kurzweil integrable function on an m -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function f [ 0 , 1 ] 2 ⟶ ℝ and a continuous function F [ 0 , 1 ] 2 ⟶ ℝ such that ( ) ∫ 0 x ( ) ∫ 0 y f ( u , v ) d v d u = ( ) ∫ 0 y ( ) ∫ 0 x f ( u , v ) d u d v = F ( x , y ) for all ( x , y ) ∈ [ 0 , 1 ] 2 .