### Henstock-Kurzweil Integration: Its Relation to Topological Vector Spaces

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Lectures on the Theory of Integration. Singapore: World Scientific. Kurzweil, J. Lee, P.

Cambridge: Cambridge University Press. Lu, J. The primitive of Henstock integrable functions in Euclidean space.

## An Introduction to the Gauge Integral

London Math. Society Muldowney , P. Pitman Research Notes in Mathematics Series. Harlow: Longman. Boundary Value Problems December , Cite as. On second order nonlinear boundary value problems and the distributional Henstock-Kurzweil integral. Open Access.

First Online: 01 May Definition 2. Example 2.

## Henstock-Kurzweil Integration

Lemma 2. Lemma 3. Proof In view of Eq.

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Theorem 3. Example 4. Remark 4.

Leela, S: Monotone method for second order periodic boundary value problems. Nonlinear Anal.

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Zhou, X, Ye, G: Second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. Pure Math. Nonlinear Differ. The main results: there exists a topology U on P such that 1 P,U is a topological vector space, 2 P,U is complete, and 3 every E-convergent sequence is convergent in P,U.

On the other hand, there is no topology U fulfilling 2 , 3 and P,U being a locally convex space.

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