N. Albuquerque

A Levin-Milman theorem for Young variation

In 1940, Levin\footnotemark[1] and Milman proved that a closed linear subspace of $C[0,1]$ whose elements all have bounded Jordan variation must be finite-dimensional. We prove its analogue for variation in the sense of Young and, more generally, for every finite-valued nondecreasing gauge $\varphi:[0,\infty)\to[0,\inf...