Taylor's theorem for a function of several variablesClassroom notes

In this note the measure problem for the Lebesgue measure is discussed in terms of metric space theory. It is illuminated that under the axiom of choice most of the subsets of 0, 1) with positive outer measure are non‐Lebesgue measurable. This fact is adequate to emphasize the significance of Lebesgue measurability as well as the essentiality of the axiom of choice.