A weak quasi-Lindelöf property and quasi-fine supports of measures (Q1891222)

We show that the fine topology of a right Markov process always enjoys a weak form of Doob's quasi-Lindelöf property. Using this property, we construct \(\lambda\)-quasi-fine supports for measures not charging \(\lambda\)-semipolar sets, where \(\lambda\) is a fixed initial distribution. We provide several other applications of the weak quasi-Lindelöf property, including a positive answer to a question posed by Dellacherie.