This is a result that appear on Stochastic Integration And Differential Equation of Philip Protter. The author define $\Vert \mu \Vert $ where $\mu = \mathcal{L}(X_{0})$ ( The law of $X_{0}$). I have never seen a notation like that before. Could someone help me to know what it means? I have been looking at many books but unfortunately, I have not obtained an answer.
What the author means by usual hypotheses is this:
