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local uniform convergence

uniform convergence on a neighborhood of each point

en-US/ˈloʊkəl ˈjunəˌfɔɹm kənˈvɝd͡ʒəns/
en-GB/ˈləʊkl ˈjuːnɪfɔːm kənˈvɜːd͡ʒəns/

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uniform convergence