Peano–Jordan measure
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In mathematics, the Peano measure (also known as the Peano content) is an extension of the notion of size (length, area, volume) to shapes more complicated than, for example, a triangle, disk, or parallelepiped.
It turns out that for a set to have Peano content it should be well-behaved in a restrictive sense. For this reason, it is now more common to work with the Lebesgue measure, which is an extension of the Peano content to a larger class of sets. Historically speaking, Peano content came first, towards the end of the nineteenth century. For historical reasons, the term Peano measure is now well-established for this set function, despite the fact that it is not a true measure in its modern definition, since sets with Peano content do not form a σ-algebra. For example, singleton sets in each have a Peano content of 0, while , a countable union of them, does not have Peano content.[1] For this reason, some authors[2] use the term Peano content.
The Peano measure is named after its originators, the Italian mathematician Giuseppe Peano.[3]