Question

Assume that 𝛼 is increasing on [𝑎, 𝑏]. Note that if 𝑓 ∈ 𝑅(𝛼) on [𝑎, 𝑏], then 𝑓2 ∈ 𝑅(𝛼) on [𝑎, 𝑏]. Use this statement to prove that if 𝑓, 𝑔 ∈ 𝑅(𝛼) on [𝑎, 𝑏], then 𝑓𝑔 ∈ 𝑅(𝛼) on[𝑎,𝑏].