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Definition

A $\sigma$-frame is a $\sigma$-complete lattice $(L, \leq, \bot, \vee, \top, \wedge, \Vee)$ with a family of dependent terms

representing the countably infinitary distributive property for the lattice.

Examples

• Sierpinski space, denoted as $\Sigma$ or $1_\bot$, is the initial $\sigma$-frame.

See also

• sigma-complete lattice

• distributive lattice

• measure

• probability measure

• Dedekind real numbers

References

• Alex Simpson, Measure, randomness and sublocales.

• Univalent Foundations Project, Homotopy Type Theory – Univalent Foundations of Mathematics (2013)