A quantitative condensation of singularities on arbitrary sets

AbstractThis paper deals with quantitative extensions of the classical condensation principle of Banach and Steinhaus to arbitrary (not necessarily countable) families of sequences of operators. Some applications concerned with the sharpness of approximation processes, with (Weierstrass) continuous nondifferentiable functions as well as with the classical counterexample of Marcinkiewicz on the divergence of Lagrange interpolation polynomials, illustrate this unifying approach to various condensations of singularities in analysis