Metric functionals and weak convergence

Armando W. Gutiérrez; Olavi Nevanlinna

Metric functionals and weak convergence

Armando W. Gutiérrez, Olavi Nevanlinna

BA4702 Design and operation of energy systems

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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 the 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.

Original language	English
Journal	arXiv preprint
Publication status	Submitted - 2025
MoE publication type	Not Eligible

Keywords

metric functional
metric geometry
weak convergence

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dWeakConvergenceSubmitted manuscript, 292 KB

https://arxiv.org/pdf/2506.04154

MOPO: Comprehensive, fast, user-friendly and thoroughly validated open-source energy system planning framework
Kiviluoma, J. (PI), Helistö, N. (PI), Rasku, T. (Participant), Soininen, A. (Participant), Savolainen, P. T. (Participant), Ikäheimo, J. (Participant), Putkonen, N. (Participant), Louis, J.-N. (Participant) & Gutierrez, A. W. (Participant)
1/01/23 → 31/12/26
Project: EU project

Cite this

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title = "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 the 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.",

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N2 - 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 the 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.

AB - 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 the 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.

KW - metric functional

KW - metric geometry

KW - weak convergence

M3 - Article

JO - arXiv preprint

JF - arXiv preprint

ER -

Metric functionals and weak convergence

Abstract

Keywords

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MOPO: Comprehensive, fast, user-friendly and thoroughly validated open-source energy system planning framework

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