Measure zero Guide, Meaning , Facts, Information and Description

A set of numbers has measure zero if its Lebesgue measure is zero. A classic example is the set of rational numbers in the real line under standard (Euclidean) Lebesgue measure. As another example, a monotonic function on the real line is continuous everywhere except on a set of measure zero.

See also

• measure
• Almost everywhere
• Cantor function
• Euclidean space
• Measure (mathematics)
• Outer measure
• Real analysis

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