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Riemann Integrabe Step Functions

  1. Mar 12, 2013 #1
    Suppose that [itex]g:[a,b]\rightarrow[c,d][/itex] is Riemann integrable on [itex][a,b][/itex] and [itex]f:[c,d]\rightarrow ℝ[/itex] is Riemann integrable on [itex][c,d][/itex]. Prove that [itex]f\circ g[/itex] is Riemann integrable on [itex][a,b][/itex] if either [itex]f[/itex] or [itex]g[/itex] is a step function.

    The proof for [itex]g[/itex] being a step function seems easy enough, but the other way seems much trickier. Thoughts?
  2. jcsd
  3. Mar 12, 2013 #2


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    Science Advisor

    Have you tried doing a formal composition:

    ciχAi °g

    And then extending by linearity to

    Ʃk=1nckχAkog ?
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