  Shapiro's lethargy theorem states that if {A_n} is any non-trivial linear
approximation scheme on a Banach space X, then the sequences of errors of best
approximation E(x,A_n) = \inf_{a \in A_n} ||x - a_n||_X decay almost
arbitrarily slowly. Recently, Almira and Oikhberg investigated this kind of
result for general approximation schemes in the quasi-Banach setting. In this
paper, we consider the same question for F-spaces with non decreasing metric d.
We also provide applications to the rate of decay of s-numbers, entropy
numbers, and slow convergence of sequences of operators.
