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We show that, generally, families of measurable functions do not have the difference property under some assumption. We also show that there are natural classes of functions which do not have the difference property in ZFC. This extends the result of Erdős concerning the family of Lebesgue measurable functions.
Rafał Filipów. "On the difference property of families of measurable functions." Colloquium Mathematicae 97.2 (2003): 169-180. <http://eudml.org/doc/285220>.
@article{RafałFilipów2003, abstract = {We show that, generally, families of measurable functions do not have the difference property under some assumption. We also show that there are natural classes of functions which do not have the difference property in ZFC. This extends the result of Erdős concerning the family of Lebesgue measurable functions.}, author = {Rafał Filipów}, journal = {Colloquium Mathematicae}, keywords = {difference property; measurable sets; measurable functions; almost invariant sets; group}, language = {eng}, number = {2}, pages = {169-180}, title = {On the difference property of families of measurable functions}, url = {http://eudml.org/doc/285220}, volume = {97}, year = {2003}, }
TY - JOUR AU - Rafał Filipów TI - On the difference property of families of measurable functions JO - Colloquium Mathematicae PY - 2003 VL - 97 IS - 2 SP - 169 EP - 180 AB - We show that, generally, families of measurable functions do not have the difference property under some assumption. We also show that there are natural classes of functions which do not have the difference property in ZFC. This extends the result of Erdős concerning the family of Lebesgue measurable functions. LA - eng KW - difference property; measurable sets; measurable functions; almost invariant sets; group UR - http://eudml.org/doc/285220 ER -