EDB — 1J1

Exercises

1. [1J1]Find an example of functions \(f_ n:[0,1]→[0,1]\) continuous, bounded, and such that \(f_ n(x)↘_ n f(x)\) pointwise to \(f:[0,1]→[0,1]\) (i.e. for every \(x\) and \(n\) we have \(0≤ f_{n+1}(x) ≤ f_{n}(x)≤ 1\) and \(\lim _ n f_ n(x) =f(x)\)) but \(f\) is not continuous and the convergence \(f_ n→ f\) is not uniform.

   Solution 1

   [1J2]↺↻