extendedvalued
Extendedvalued is a term used in mathematics to describe objects whose value range is allowed to include an infinite value. It commonly appears in three related contexts: extended real-valued functions, extended-valued measures, and extended valuations in field theory. In each case, the additional infinity value serves to compactly describe limiting behavior, divergence, or zero elements.
In analysis, an extended-valued function is a map f from a set X to the extended real
In measure theory, measures can be extended to take infinite values. A measure μ on a measurable
In valuation theory, an extended-valued valuation v: K → Γ ∪ {∞} assigns ∞ to zero and obeys v(xy) = v(x) + v(y)
See also extended real numbers, valuation, and measure theory.