„Valós értékű függvény” változatai közötti eltérés

<math>{\mathcal F}(X,{\mathbb R}) </math> egy [[részbenrendezett gyűrű]].

 

{{see also|Borel function}}

The [[σ-algebra]] of [[Borel set]]s is an important structure on real numbers. If {{mvar|X}} has its σ-algebra and a function {{mvar|f}} is such that the [[preimage]] {{math|''f'' ⁻¹(''B'')}} of any Borel set {{mvar|''B''}} belongs to that σ-algebra, then {{mvar|f}} is said to be [[measurable function|measurable]]. Measurable functions also form a vector space and an algebra as explained [[#In general|above]].

== Other appearances ==

Other contexts where real-valued functions and their special properties are used include [[monotonic function]]s (on [[ordered set]]s), [[convex function]]s (on vector and [[affine space]]s), [[harmonic function|harmonic]] and [[subharmonic function|subharmonic]] functions (on [[Riemannian manifold]]s), [[analytic function]]s (usually of one or more real variables), [[algebraic function]]s (on real [[algebraic variety|algebraic varieties]]), and [[polynomial]]s (of one or more real variables).

==Lásd még==

* [[Valós analízis]]