Difference between revisions of "Simple function (measure theory)/Definition"

From Maths
Jump to: navigation, search
(Created page with "<noinclude> ==Definition== </noinclude> A ''simple function'' {{M|f:X\rightarrow\mathbb{R} }} on a measurable space {{M|(X,\mathcal{A})}} is a{{rMIAMRLS}}: * function of t...")
(No difference)

Revision as of 07:16, 12 March 2016

Definition

A simple function f:XR on a measurable space (X,A) is a[1]:

  • function of the form Ni=1xi1Ai(x) for
  • finitely many sets, A1,,ANA and
  • finitely many x1,,xnR

References

  1. Jump up Measures, Integrals and Martingales - René L. Schilling