  We introduce and study various notions of amenability continuous (Borel)
partial actions of locally compact (Borel) groups $G$ on topological (standard
Borel) spaces. We also study amenability of partial representations of a
locally compact group in a Banach space and show that a partial action on a
measure space is amenable iff the corresponding Koopman partial representation
on the corresponding $L^2$-space is amenable. We introduce the notion of
induced partial representation from a closed subgroup and explore perseverance
of amenability type properties under induction.
