Measurable space

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Definition

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

• $(X,\mathcal{A})$

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

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 $X$ and a $\sigma$-algebra $\mathcal{A}$, which we denote:

• $(X,\mathcal{A})$

Pre-measurable space

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

• $(X,\mathcal{A})$

See also

• Pre-measure space
• Measure space
• Measurable map