Metric Functionals and Weak Convergence
Abstract
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all metric functionals defined on said space. When restricted to bounded sequences in normed linear spaces, we prove that our notion of weak convergence agrees with the standard one.
Type
Publication
Zeitschrift für Analysis und ihre Anwendungen
Status
Peer-reviewed
Open access
Main results
Authors
Research Scientist
I’m a Researcher in Mathematics. I’ve carried out research at Aalto University, Inria Saclay, and VTT. I’ve made contributions to metric geometry, functional analysis and optimization. I’m passionate about quantum computing, risk analysis and optimization algorithms.