For a $2n$-dimensional symplectic manifold $(M,\omega)$, define its Gromov width by
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\begin{align*}
c_G(M,\omega)=\sup\{\pi r^2:r>0\text{ and there exists a smooth embedding }\varphi:B^{2n}(r)\to M\text{ with }\varphi^*\omega=\omega_0\}.
\end{align*}
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Then $c_G$ is a symplectic capacity on the class of $2n$-dimensional symplectic manifolds in the following explicit sense. If $(M,\omega)$ and $(N,\eta)$ are $2n$-dimensional symplectic manifolds and there is a smooth embedding $F:M\to N$ satisfying $F^*\eta=\omega$, then