  In this paper, we mainly derive monotonicity formula of generalized map using
conservation law, including $\phi$-$F$ harmonic map coupled with $\phi$-$F$
symphonic map with $m$ form and potential from metric measure space, $ p $
harmonic map with potential , $ V $ harmonic map with potential. As an
corollary, we can derive Liouville theorem for these maps under some finite
energy conditons. We also get Liouville type theorem for $\phi$-$F$ harmonic
map coupled with $\phi$-$F$ symphonic map under asymptotic conditon on metric
measure space. We also get Liouville theorem for $\phi$-$F$-$V$-harmonic maps
in terms of the upper bound of Ricci curvature and the bound about sectional
curvature on metric measure space. We also get Liouville theorem for $\phi$-$ F
$-harmonic map without using monotonicity formula on metric measure space.
