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...e basic concept of '''measure theory''', which studies the properties of [[sigma algebra|σ-algebras]], measures, [[measurable function]]s and [[integral]]s. ...pparent paradox. To deal with such problems one developes the concept of [[sigma algebra|σ-algebra]], a family of subsets to which it is possible to assign a

...atical concepts such as [[set|sets]], [[measure (mathematics)|measure]], [[sigma algebra|sigma algebras]] and a set of rules we expect probability to follow, known

...ility distributions are actually defined much more generally in terms of [[sigma algebra|sigma algebras]] and [[measure|measures]]. Using these general definitions, *[[Sigma algebra]]

...tstyle \{\mathcal{F}_t\}_{t \in T}</math> be an increasing family of sub-[[sigma algebra|<math>\scriptstyle \sigma</math>-algebras]] of <math>\scriptstyle \mathcal{

...(\mathbb{R}),P)</math> where <math>\mathcal{B}(\mathbb{R})</math> is the [[sigma algebra]] of [[Borel set|Borel subsets]] of <math>\mathbb{R}</math> and ''P'' is a

...athbb{C}^n))</math>, where <math>\mathcal{B}(\mathbb{C}^n)</math> is the [[sigma algebra]] of [[Borel set|Borel sets]] of <math>\mathbb{C}^n</math>. A formal defini

*[[Sigma algebra]]

*[[Sigma algebra]]