I have a question, please. If I have a cadlag which could cross this increasing sequences of intervals say [0, Sn], in the paper that I am reading, it says that this cadlag cannot cross this interval infinitely many times in finite time, it should cross in infinite time. I did not understand the statement, can you explain it please ?

Thanks ]]>

thank you very much for your answer.

For everyone reading this I also found a reference for an even slightly more general version in Bogachev’s Measure Theory Corollary 6.9.12 (due to Leese):

$X$ a Souslin space (eg Polish), $\Omega$ any measurable space and $S$ an analytic/Souslin-B subset of $\Omega \times X$ (eg any measurable set). Then:

$\pi(S)$ is Souslin-B in $\Omega$ (thus universally measurable) and there exists a section that is measurable wrt the $\sigma$-algebra generated by Souslin-B sets (in particular universally measurable).

It would be nice if one could get rid of all the topological conditions and just work with universally measurable spaces, maps and subsets.

George, do you see any way to generalize further?

Thank you for your great blog.

]]>