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  "body": "\n## Summary\n\nIn group theory, given a group $G$, a **quasimorphism** (or **quasi-morphism**) is a [[function|0EPAT51DXQ]] $f:G\\to\\mathbb{R}$ which is additive up to bounded error, i.e. there exists a constant $D\\geq 0$ such that $|f(gh)-f(g)-f(h)|\\leq D$ for all $g, h\\in G$. The least positive value of $D$ for which this inequality is satisfied is called the **defect** of $f$, written as $D(f)$. For a group $G$, quasimorphisms form a [[subspace|00YC1D652K]] of the [[function space|0GZB2SN0PH]] $\\mathbb{R}^G$.\n",
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