In mathematics, an ultralimit is a geometric construction that assigns a limit metric space to a sequence of metric spaces X n {\displaystyle X_{n}} ....

since the ultralimit coincides with the regular limit when it exists. μ {\displaystyle \mu } is finitely additive. This is since ultralimits commute with...

considered. In model theory, this construction can be referred to as an ultralimit or limiting ultrapower. Beginning with a structure, A 0 {\displaystyle...

reformulated by Gromov and others into the more flexible notion of an ultralimit.[G93] Gromov's compactness theorem had a deep impact on the field of geometric...

the sequence 0.9, 0.99, 0.999, ...‍. A different definition involves an ultralimit, i.e., the equivalence class [(0.9, 0.99, 0.999, ...)] of this sequence...

trees arise as limits of various random processes on finite trees. Any ultralimit of a sequence ( X i ) {\displaystyle (X_{i})} of δ i {\displaystyle \delta...

scale geometry of the group. Asymptotic cones are particular examples of ultralimits of metric spaces. Gödel's ontological proof of God's existence uses as...

An ultralimit is a geometric construction that assigns to a sequence of metric spaces Xn a limiting metric space. An important class of ultralimits are...

Carnot–Carathéodory metrics have metric dilations; they are asymptotic cones (see Ultralimit) of finitely-generated nilpotent groups, and of nilpotent Lie groups,...

where W 1 {\displaystyle W_{1}} is the first Wasserstein distance. any ultralimit or 1-Lipschitz retraction of the above. Every consistent conical geodesic...

Mathematical Society. ISBN 978-1-4704-1104-6. MR 3753580. Geometric group theory Ultralimit Tree-graded space Kazhdan's property (T) Cornelia Druțu. "Cornelia Druţu's...