Strong Fubini properties for measure and category

Krzysztof Ciesielski, and Miklós Laczkovich. "Strong Fubini properties for measure and category." Fundamenta Mathematicae 178.2 (2003): 171-188. <http://eudml.org/doc/283043>.

@article{KrzysztofCiesielski2003,
abstract = {Let (FP) abbreviate the statement that $∫_\{0\}^\{1\} (∫_\{0\}^\{1\} fdy)dx = ∫_\{0\}^\{1\} (∫_\{0\}^\{1\} fdx)dy$ holds for every bounded function f: [0,1]² → ℝ whenever each of the integrals involved exists. We shall denote by (SFP) the statement that the equality above holds for every bounded function f: [0,1]² → ℝ having measurable vertical and horizontal sections. It follows from well-known results that both of (FP) and (SFP) are independent of the axioms of ZFC. We investigate the logical connections of these statements with several other strong Fubini type properties of the ideal of null sets. In particular, we establish the equivalence of (SFP) to the nonexistence of certain sets with paradoxical properties, a phenomenon that was already known for (FP). We also give the category analogues of these statements and, whenever possible, we try to put the statements in a setting of general ideals as initiated by Recław and Zakrzewski.},
author = {Krzysztof Ciesielski, Miklós Laczkovich},
journal = {Fundamenta Mathematicae},
keywords = {strong Fubini property; null sets; sets with paradoxical properties; category; general ideals},
language = {eng},
number = {2},
pages = {171-188},
title = {Strong Fubini properties for measure and category},
url = {http://eudml.org/doc/283043},
volume = {178},
year = {2003},
}

TY - JOUR
AU - Krzysztof Ciesielski
AU - Miklós Laczkovich
TI - Strong Fubini properties for measure and category
JO - Fundamenta Mathematicae
PY - 2003
VL - 178
IS - 2
SP - 171
EP - 188
AB - Let (FP) abbreviate the statement that $∫_{0}^{1} (∫_{0}^{1} fdy)dx = ∫_{0}^{1} (∫_{0}^{1} fdx)dy$ holds for every bounded function f: [0,1]² → ℝ whenever each of the integrals involved exists. We shall denote by (SFP) the statement that the equality above holds for every bounded function f: [0,1]² → ℝ having measurable vertical and horizontal sections. It follows from well-known results that both of (FP) and (SFP) are independent of the axioms of ZFC. We investigate the logical connections of these statements with several other strong Fubini type properties of the ideal of null sets. In particular, we establish the equivalence of (SFP) to the nonexistence of certain sets with paradoxical properties, a phenomenon that was already known for (FP). We also give the category analogues of these statements and, whenever possible, we try to put the statements in a setting of general ideals as initiated by Recław and Zakrzewski.
LA - eng
KW - strong Fubini property; null sets; sets with paradoxical properties; category; general ideals
UR - http://eudml.org/doc/283043
ER -