Define the space
β1([a,b]) as the space of functions
f:[a,b]↦R which are everywhere differentiable and whose derivative
f′ is a bounded function. One equips this space with the metric
Prove that this turns
β1([a,b]) into a complete metric space.
Please help. I know what a complete metric space is, but I'm having trouble getting started with this proof. I would prefer a hint that would point me in the right direction as I'd like the opportunity to work through the proof myself, but I'll be thankful for any help I receive.