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locally integrable function

function which is integrable on every compact subset of its domain of definition

en-GB/ˈləʊkəlɪ ɪntɪɡɹəbl ˈfʌŋkʃn/
en-US/ˈloʊkəli ˈɪntəɡɹəbəl ˈfʌŋkʃən/

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function