Math 2.0

concept

Jordan measure

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.

What this node needs for W2
  • 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)

The writing levels say how complete the text of a node is. They do not measure its truth.

What this needs

To read this node, read these 5 nodes in this order. The foundations come first, and the list ends with this node.

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 node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Function of several variables concept
  4. Double integral concept
  5. Jordan measure concept

What depends on this

3 nodes use this node, directly or through other nodes.

Sources

  1. Web https://en.wikipedia.org/wiki/Peano%E2%80%93Jordan_measure, Extension to more complicated sets

What links here

Definitions

Used by