A problem related to the continuum hypothesis which was solved by Solovay (1970) using the inaccessible cardinals axiom. It has been proven by Shelah and Woodin (1990) that use of this axiom is essential to the proof.
Lebesgue Measurability Problem
See also
Continuum Hypothesis, Inaccessible Cardinals Axiom, Lebesgue MeasureExplore with Wolfram|Alpha
References
Shelah, S. and Woodin, H. "Large Cardinals Imply that Every Reasonable Definable Set of Reals is Lebesgue Measurable." Israel J. Math. 70, 381-394, 1990.Solovay, R. M. "A Model of Set-Theory in which Every Set of Reals is Lebesgue Measurable." Ann. Math. 92, 1-56, 1970.Referenced on Wolfram|Alpha
Lebesgue Measurability ProblemCite this as:
Weisstein, Eric W. "Lebesgue Measurability Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LebesgueMeasurabilityProblem.html