Can anyone prove that the product of two Lipschitz functions is itself Lipschitz? ( Lipschitz : a function f such that for all x,y in D, there exists an L > 0 s.t. d( f(x), f(y) ) <= L*d( x,y ) )
Can anyone prove that the product of two Lipschitz functions is itself Lipschitz? ( Lipschitz : a function f such that for all x,y in D, there exists an L > 0 s.t. d( f(x), f(y) ) <= L*d( x,y ) )
This is not true: take (absolute value) is Lipschitz but is not. If is bounded however use