nLab probability valuation

Definition

In measure theory, a probability valuation on a lattice $(L, \leq, \bot, \vee, \top, \wedge)$ is a monotonic function $\mu:L \to [0, 1]$ such that $\mu(\bot) = 0$, $\mu(\top) = 1$, and the modularity condition is satisfied: for all elements $a, b \in L$,

$$\mu(a) + \mu(b) = \mu(a \wedge b) + \mu(a \vee b)$$

See also

• unit interval

• valuation (measure theory)

• sigma-continuous probability valuation

References

• Alex Simpson, Measure, randomness and sublocales.