Causality
Definition: an LTI system is causal if only past and present values affect the output.
Example to satisfy this property:
$ h(t) = t*e^{-t}*u(t) $
h(t) = 0 for t < 0 because u(t) = 0 for t < 0 Thus, this system exemplifies causality.
Example that does not satisfy this property:
$ h(t) = e^{2t}u(-1-t) $ $ u(-1-t) \neq 0 $ for t < 0 $ \Rightarrow h(t)\neq 0 $ for t < 0
Thus, the system does not exemplify causality.