In measure theory, the **Lebesgue measure**, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of *n*-dimensional Euclidean space. For *n* = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called ** n-dimensional volume**,

**, or simply**

*n*-volume**volume**. It is used throughout real analysis, in particular to define Lebesgue integration. Sets that can be assigned a Lebesgue measure are called

**Lebesgue measurable**; the measure of the Lebesgue measurable set

*A*is denoted by λ(

*A*).

Henri Lebesgue described this measure in the year 1901, followed the next year by his description of the Lebesgue integral. Both were published as part of his dissertation in 1902.

The Lebesgue measure is often denoted *dx*, but this should not be confused with the distinct notion of a volume form.

Read more about Lebesgue Measure: Definition, Examples, Properties, Null Sets, Construction of The Lebesgue Measure, Relation To Other Measures

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“Both the man of science and the man of art live always at the edge of mystery, surrounded by it. Both, as a *measure* of their creation, have always had to do with the harmonization of what is new with what is familiar, with the balance between novelty and synthesis, with the struggle to make partial order in total chaos.... This cannot be an easy life.”

—J. Robert Oppenheimer (1904–1967)