There were various proofs of the discrete martingale convergence theorem, but as far as I know there is only one proof of the continuous version of this theorem using the up-crossing lemma.
I wrote a paper that provides a new proof of the continuous martingale convergence theorem avoiding the up-crossing lemma. Also following this approach provides a new proof for the convergence of an integrable reversed discrete sub-martingale and versions of the regularization theorems.
Do you have ideas-suggestions if this could be publishable and where.
Preprint of the paper can be found here: https://arxiv.org/abs/2107.00006
