In descriptive set theory, a tree over a product set Y × Z {\displaystyle Y\times Z} is said to be homogeneous if there is a system of measures ⟨ μ s ∣ s ∈ < ω Y ⟩ {\displaystyle \langle \mu _{s}\mid s\in {}^{<\omega }Y\rangle } such that the following conditions hold: μ s {\displaystyle \mu _{s}} is a countably-additive measure on { t ∣ ⟨ s, t ⟩ ∈ T } {\displaystyle \{t\mid \langle s,t\rangle \in T\}}. Wikipedia