Let \(\left(X_{t}ight)_{t \in I}\) and \(\left(Y_{t}ight)_{t \in I}\) be two processes with the same index set \(I \subset[0, \infty)\) and state space. Show that

\[X, Y \text { indistinguishable } \Longrightarrow X, Y \text { modifications } \Longrightarrow X, Y \text { equivalent. }\]

Assume that the processes are defined on the same probability space and \(t \mapsto X_{t}\) and \(t \mapsto Y_{t}\) are right continuous (or that \(I\) is countable). Do the reverse implications hold, too?