Spline characterizations of the Radon-Nikodým-property
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
Analysis Seminar 2018, June 8-10, Traunkirchen
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
A Banach space $X$ is said to have the Radon-Nikodým-property (RNP) if, for measures with values in $X$, the Radon-Nikodým theorem is true, i.e. if for every positive measure $\mu$ and for every $\mu$-continuous measure $\nu$ of bounded variation with
values in $X$, there exists an integrable function $f$ with values in $X$ so that $\nu(A) = \int_A f d\mu$ for every measurable set $A$. The RNP can be characterized in terms of Martingale convergence, i.e., for a Banach space $X$, all $L^1$-bounded
martingales $(f_n)$ with values in $X$ converge almost surely if and only if $X$ has the RNP.
In this talk, we give a similar characterization of the RNP
in terms of polynomial spline sequences instead of martingales.