Measurable space

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Definition

Given a set, [ilmath]X[/ilmath], and a [ilmath]\sigma[/ilmath]-algebra, [ilmath]\mathcal{A}\in\mathcal{P}(\mathcal{P}(X))[/ilmath] then a measurable space is the tuple:

• [ilmath](X,\mathcal{A})[/ilmath]

This is not to be confused with a measure space which is a [ilmath]3[/ilmath]-tuple: [ilmath](X,\mathcal{A},\mu)[/ilmath] where [ilmath]\mu[/ilmath] is a measure on the measurable space [ilmath](X,\mathcal{A})[/ilmath]

Premeasurable space

1. REDIRECT Pre-measurable space/Definition

See also

• Pre-measurable space
• Measure space
  • Measure
  • Measurable map

OLD PAGE

Definition

A measurable space is a tuple consisting of a set [ilmath]X[/ilmath] and a [ilmath]\sigma[/ilmath]-algebra [ilmath]\mathcal{A} [/ilmath], which we denote:

• [ilmath](X,\mathcal{A})[/ilmath]

Pre-measurable space

A pre-measurable space is a set [ilmath]X[/ilmath] coupled with an algebra, [ilmath]\mathcal{A} [/ilmath] (where [ilmath]\mathcal{A} [/ilmath] is NOT a [ilmath]\sigma[/ilmath]-algebra) which we denote as follows:

• [ilmath](X,\mathcal{A})[/ilmath]

See also

• Pre-measure space
• Measure space
• Measurable map