Math 2.0

Measure and integration Construction of measures Concept

Jordan measure

Builds on Euclidean spaceDouble integral

Summary

The Jordan measure, or Jordan content, extends the volume of boxes in R^n to some bounded sets. Finite unions of boxes approximate these sets well from inside and from outside. A bounded set has Jordan measure exactly when its indicator function is Riemann integrable, and then the measure is the integral of that function.

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Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptFunction of several variables, concept, no evidence levelFunction of several v…conceptDouble integral, concept, no evidence levelDouble integralconceptJordan measure, concept, no evidence levelJordan measureconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Function of several variables concept
  4. Double integral concept
  5. Jordan measure concept

Where this leads

4 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Peano%E2%80%93Jordan_measure, Extension to more complicated sets
About this page
Tag0KTGJW1ZTH
URIm2://0KTGJW1ZTH
Aliasesjordan-content, peano-jordan-measure
Kindconcept
WritingW1 stated
MSC28A75
UsesEuclidean space, Double integral
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  • edge instance_of in: at least two examples (0 of 2)
  • edge not_instance_of in: at least one non-example (0 of 1)
  • edge specializes both: the more general notions and the special cases (0 of 1)

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