Let H = {ei : i∈ I} be a Hamel basis in R whose Lebesgue measure is zero (see Theorem 3). For any natural number n, we denote by En the setof all those elements e=∑i∈Iqiei (qi∈ Q)which...
We build a new class of Banach function spaces, whose function norm isρ(p[⋅],δ[⋅](f)=inff=∑k=1∞fk∑k=1∞essinfx∈(0,1)ρp(x)(δ(x)−1fk(⋅)), where ρp(x) denotes the norm of the Lebesgue space of exponent p(x) (assumed measurable and possibly infinite...