Rearrangement-invariant hulls of weighted Lebesgue spaces

We characterize the rearrangement-invariant hull, with respect to a given measure $\mu$, of weighted Lebesgue spaces. The solution leads us to first consider when this space is contained in the sum of $(L^1+L^{\mathrm{\infty }})(R,\mu )$ and the final condition is given in terms of embeddings for weighted Lorentz spaces.