Editing Measure space (section)

==Example==

Set <math>X = \{0, 1\}</math>. The <math display=inline>\sigma</math>-algebra on finite sets such as the one above is usually the [[power set]], which is the set of all subsets (of a given set) and is denoted by <math display=inline>\wp(\cdot).</math> Sticking with  this convention, we set
<math display=block>\mathcal{A} = \wp(X)</math>

In this simple case, the power set can be written down explicitly:
<math display=block>\wp(X) = \{\varnothing, \{0\}, \{1\}, \{0, 1\}\}.</math>

As the measure, define <math display=inline>\mu</math> by 
<math display=block>\mu(\{0\}) = \mu(\{1\}) = \frac{1}{2},</math>
so <math display=inline>\mu(X) = 1</math> (by additivity of measures) and <math display=inline>\mu(\varnothing) = 0</math> (by definition of measures).

This leads to the measure space <math display=inline>(X, \wp(X), \mu).</math> It is a [[probability space]], since <math display=inline>\mu(X) = 1.</math> The measure <math display=inline>\mu</math> corresponds to the [[Bernoulli distribution]] with <math display=inline>p = \frac{1}{2},</math> which is for example used to model a fair coin flip.