- #1
Arkuski
- 40
- 0
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?
The proof for [itex]g[/itex] being a step function seems easy enough, but the other way seems much trickier. Thoughts?