On the variation of the Bernstein polynomials of a function of unbounded variation

Kantorovitch Polynomials Diminish Generalized Length

“…However the Bernstein polynomials behave erratically for discontinuous functions and in particular VB n f\>Vf for most discontinuous functions. There exist badly discontinuous functions/such that Vf=co but such that VB n f-> 0 [4].…”