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MATHEMATICA BOHEMICA, Vol. 127, No. 1, pp. 15-26 (2002)
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# Substitution formulas for the Kurzweil and Henstock vector integrals

## M. Federson

* M. Federson*, Universidade de Sao Paulo, Departamento de Matematica, Sao Carlos, CP 688, CEP 13560-970, Sao Carlos-SP, Brazil, e-mail: ` federson@icmc.sc.usp.br`

**Abstract:**
Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains that of Henstock. In the present paper, we consider abstract vector integrals of Kurzweil and prove Substitution Formulas by functional analytic methods. In general, Substitution Formulas need not hold for Kurzweil vector integrals even if they are defined.

**Keywords:** Kurzweil-Henstock integrals, integration by parts, integration by substitution

**Classification (MSC2000):** 26A39

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