Let $T^{k}$ act effectively on $X$, $k\leq n-1$. Suppose that there is a continuous map $G:X\rightarrow M$ to an $(n-k)$-dimensional manifold $M$ such that $G(T\cdot x)=G(x)$ for all $T\in T^{k}$. Suppose that for $t$ in a dense subset of $\mu(X)$ the induced maps $G_{t}:X_{t}\rightarrow M$ have fibres that are Lagrangian with respect to $\omega_{t}$. Then $f:X\rightarrow\mu(X)\times M$ given by:

$$f=(\mu,G)$$

(23)

defines a $T^{k}$-invariant Lagrangian fibration.