# Sh:947

- Larson, P. B., Neeman, I., & Shelah, S. (2010).
*Universally measurable sets in generic extensions*. Fund. Math.,**208**(2), 173–192. arXiv: 1003.2479 DOI: 10.4064/fm208-2-4 MR: 2640071 -
Abstract:

A subset of a topological space is said to be universally measurable if it is measurable with respect to every complete, countably additive \sigma-finite measure on the space, and universally null if it has measure zero for each such atomless measure. In 1934, Hausdorff proved that there exist universally null sets of cardinality \aleph_1, and thus that there exist a least 2^{\aleph_1} such sets. Laver showed in the 1970’s that consistently there are just continuum many universally null sets. The question of whether there exist more than continuum many universally measurable sets was asked by Mauldin no later than 1984. We show that consistently there exist only continuum many universally measurable sets. - published version (20p)

Bib entry

@article{Sh:947, author = {Larson, Paul B. and Neeman, Itay and Shelah, Saharon}, title = {{Universally measurable sets in generic extensions}}, journal = {Fund. Math.}, fjournal = {Fundamenta Mathematicae}, volume = {208}, number = {2}, year = {2010}, pages = {173--192}, issn = {0016-2736}, doi = {10.4064/fm208-2-4}, mrclass = {03E35 (03E17 28A05 54H99)}, mrnumber = {2640071}, mrreviewer = {J\"org D. Brendle}, doi = {10.4064/fm208-2-4}, note = {\href{https://arxiv.org/abs/1003.2479}{arXiv: 1003.2479}}, arxiv_number = {1003.2479} }