Questions tagged [gauge-integral]

For questions about Henstock-Kurzweil integral or gauge integral.

Henstock-Kurzweil integral or gauge integral (sometimes also called generalized Riemann integral, Perron integral, Denjoy integral or Luzin integral) is a generalization of Riemann integral.

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Show that the following function has a gauge-integral and calculate its value.

We define: $$f: I = [0,1] \rightarrow \mathbb{R}: x \mapsto f(x) = \sin(x)1_{[0,1] - \mathbb{Q}} + x1_{[0,1]\cap\mathbb{Q}} $$ where $1_A$ is the characteristic function on A. Show that $f$ has a gauge integral on [0,1] and calculate it. I've come…

gauge-integral

asked Dec 23 '17 at 20:25

Digitalis