Two Ways to Define Compatible Metrics on the Simplex of Measures

2014 ◽  
Vol 196 (2) ◽  
pp. 138-143
Author(s):  
A. M. Vershik
Keyword(s):  
Compatible Metrics

scholarly journals On μ-compatible metrics and measurable sensitivity

2012 ◽  
Vol 126 (1) ◽  
pp. 53-72 ◽  
Author(s):  
Ilya Grigoriev ◽  
Marius Cătălin Iordan ◽  
Amos Lubin ◽  
Nathaniel Ince ◽  
Cesar E. Silva
Keyword(s):  
Compatible Metrics

scholarly journals Comparability of lower Attouch-Wets topologies

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1435-1440
Author(s):  
Marco Rosa ◽  
Paolo Vitolo
Keyword(s):  
Sufficient Conditions ◽  
Metrizable Space ◽  
Necessary And Sufficient Conditions ◽  
Compatible Metrics ◽  
Necessary And Sufficient

Beer and Di Concilio [4] have given necessary and sufficient conditions for a two-sided Attouch-Wets topology to contain another on the hyperspace of non-empty closed subsets of a metrizable space as determined by metrics compatible with the topology. In the present paper, we characterize comparability of lower Attouch-Wets topologies as determined by compatible metrics.

scholarly journals Review of Different Error Metrics: A Case of Solar Forecasting

2021 ◽  
Vol 20 (4) ◽  
pp. 158-165
Author(s):  
Pardeep Singla ◽  
Manoj Duhan ◽  
Sumit Saroha
Keyword(s):  
Power Systems ◽  
Solar Panels ◽  
Solar Forecasting ◽  
Common Error ◽  
Renewable Energy Systems ◽  
Error Measures ◽  
Error Metrics ◽  
Compatible Metrics ◽  
Modern Era ◽  
Wrong Interpretation

Renewable energy systems (RES) are no longer confined to being used as a stand-alone entity in the modern era. These RES, especially solar panels are also used with the grid power systems to supply electricity. However, precise forecasting of solar irradiance is necessary to ensure that the grid operates in a balanced and planned manner. Various solar forecasting models (SFM) are presented in the literature to produce an accurate solar forecast. Nevertheless, each model has gone through the step of evaluation of its accuracy using some error measures. Many error measures are discussed in the literature for deterministic as well as probabilistic solar forecasting. But, each study has its own selected error measure which sometimes landed on a wrong interpretation of results if not selected appropriately. As a result, this paper offers a critical assessment of several common error metrics with the goal of discussing alternative error metrics and establishing a viable set of error metrics for deterministic and probabilistic solar forecasting. Based on highly cited research from the last three years (2019-2021), error measures for both types of forecasting are presented with their basic functionalities, advantages & limitations which equipped the reader to pick the required compatible metrics

scholarly journals Topologies induced by metrics with disconnected range

1982 ◽  
Vol 25 (1) ◽  
pp. 133-142
Author(s):  
Kevin Broughan
Keyword(s):  
Metric Space ◽  
Metrizable Space ◽  
Uniform Limit ◽  
Irrational Numbers ◽  
Compatible Metrics ◽  
Completely Metrizable

In a metric space (X, d) a ball B(x, ε) is separated if d(B(x, ε), X\B(x, ε)] > 0. If the separated balls form a sub-base for the d-topology then Ind X = 0. The metric is gap-like at x if dx(X) is not dense in any neighbourhood of 0 in [0, ∞). The usual metric on the irrational numbers, P, is the uniform limit of compatible metrics (dn), each dn being gap-like on P. In a completely metrizable space X if each dense Gδ is an Fσ then Ind X = 0.

Sign in / Sign up

Export Citation Format

Share Document