Let $\mathsf{k}$ be an algebraically closed field of zero characteristic.
It is a well known result due to Gabber that for any finite dimensional algebraic Lie algebra $\mathfrak{g}$ and every finitely generated left $U(\mathfrak{g})$-module $M$ it holds an analogue of Bernstein inequality:
$ (*) \, GK \, M \geq \frac{1}{2} GK \, U(\mathfrak{g})/Ann(M) , $ where $Ann(M)$ is the left anihilator of $M$.
It is known that for some modules, inequality $(*)$ is in fact an equality. A famous result is
Theorem. When $\mathfrak{g}$ is semisimple and $M$ belongs to the category $\mathcal{O}$, equality holds in $(*)$.
Now, the only references I know of for this result are
(1) Jantzen's book: Einhüllende Algebren halbeinfacher Lie-Algebren (1983), and
(2) Joseph's (frequently cited) notes: Applications de la Thèorie des anneaux aux algèbres enveloppantes, Cours de troisième cycle. Univ. de Paris VI, unpublished mimeographed notes, 1981.
Now, I am really interested understanding the proof of the statement mentioned above, but I don't know German, and hence I find impossible to read Jantzen's book. I can read French, but unfortunately, due to coronavirus pandemic, I have no access to a physical exemplar of Joseph's work - and I couldn't find it online either.
If anyone knows an article, or lecture notes, or book, that discuss the above Theorem in certain detail, except the above (1) and (2), I would be very grateful indeed.