We prove that the property “P doesn't make the old reals Lebesgue null” is preserved under countable support iterations of proper forcings, under the additional assumption that the forcings are nep (a generalization of Suslin proper) in an absolute way. We also give some results for general Suslin ccc ideals.
"Preserving preservation." J. Symbolic Logic 70 (3) 914 - 945, September 2005. https://doi.org/10.2178/jsl/1122038920