Editing Measurable space (section)

==Common measurable spaces==

If <math>X</math> is finite or countably infinite, the <math>\sigma</math>-algebra is most often the [[power set]] on <math>X,</math> so <math>\mathcal{F} = \mathcal P(X).</math> This leads to the measurable space <math>(X, \mathcal P(X)).</math>

If <math>X</math> is a [[topological space]], the <math>\sigma</math>-algebra is most commonly the [[Borel sigma algebra|Borel <math>\sigma</math>-algebra]] <math>\mathcal B,</math> so <math>\mathcal{F} = \mathcal B(X).</math> This leads to the measurable space <math>(X, \mathcal B(X))</math> that is common for all topological spaces such as the real numbers <math>\R.</math>