A constructive integral equivalent to the integral of Kurzweil
We slightly modify the definition of the Kurzweil integral and prove that it still gives the same integral.
We slightly modify the definition of the Kurzweil integral and prove that it still gives the same integral.
We improve a theorem of C. L. Belna (1972) which concerns boundary behaviour of complex-valued functions in the open upper half-plane and gives a partial answer to the (still open) three-segment problem.
For a new Perron-type integral a concept of convergence is introduced such that the limit of a sequence of integrable functions , is integrable and any integrable is the limit of a sequence of stepfunctions , .