A process is Càdlàg (i.e. right continuous with left limits) if $$\forall\omega\in\Omega:t\mapsto X_{t}(\omega)\text{ is right continuous and has left limits everywhere}$$i.e. - the left limit $$f(t-):=\lim_{ s \uparrow t^{-} }f(s)$$ exists and; - the right limit $$f(t+):=\lim_{ s \downarrow t^{+} } f(s)$$exists and equals $f(t)$.