In group theory, given a group G {\displaystyle G} , a quasimorphism (or quasi-morphism) is a function f : G → R {\displaystyle f:G\to \mathbb {R} } which is additive up to bounded error, i.e. there exists a constant D ≥ 0 {\displaystyle D\geq 0} such that | f ( g h ) − f ( g ) − f ( h ) | ≤ D {\displaystyle |f(gh)-f(g)-f(h)|\leq D} for all g , h ∈ G {\displaystyle g,h\in G} .
In group theory, given a group G {\displaystyle G} , a quasimorphism (or quasi-morphism) is a function f : G → R {\displaystyle f:G\to \mathbb {R} } which is additive up to bounded error, i.e. there exists a constant D ≥ 0 {\displaystyle D\geq 0} such that | f ( g h ) − f ( g ) − f ( h ) | ≤ D {\displaystyle |f(gh)-f(g)-f(h)|\leq D} for all g , h ∈ G {\displaystyle g,h\in G} .
Source: Wikipedia "Quasimorphism" · CC BY-SA 4.0
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