In mathematics a **Hausdorff measure** is a type of outer measure, named for Felix Hausdorff, that assigns a number in to each set in **R***n* or, more generally, in any metric space. The zero dimensional Hausdorff measure is the number of points in the set (if the set is finite) or ∞ if the set is infinite. The one dimensional Hausdorff measure of a simple curve in **R***n* is equal to the length of the curve. Likewise, the two dimensional Hausdorff measure of a measurable subset of **R**2 is proportional to the area of the set. Thus, the concept of the Hausdorff measure generalizes counting, length, and area. It also generalizes volume. In fact, there are *d*-dimensional Hausdorff measures for any *d* ≥ 0, which is not necessarily an integer. These measures are fundamental in geometric measure theory. They appear naturally in harmonic analysis or potential theory.

Read more about Hausdorff Measure: Definition, Properties of Hausdorff Measures, Relation With Hausdorff Dimension, Generalizations

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“Nobody is glad in the gladness of another, and our system is one of war, of an injurious superiority. Every child of the Saxon race is educated to wish to be first. It is our system; and a man comes to *measure* his greatness by the regrets, envies, and hatreds of his competitors.”

—Ralph Waldo Emerson (1803–1882)