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  "body": "\n## Summary\n\nThe Daniell integral is an approach to integration that starts from a positive linear functional on a space of elementary functions.\nIt does not start from a measure.\nThe functional must satisfy a continuity condition along decreasing sequences.\nIt then extends to a large class of integrable functions, and the measure of a set appears afterwards as the integral of its indicator function.\nThis approach gives the Lebesgue integral and integrals on locally compact spaces in one framework.\n\n## Explanations\n\n### L1 human\n\nThe usual route defines lengths or areas first and integrals afterwards.\nDaniell's route goes the other way: it starts with an integral that one already knows on easy functions, such as continuous functions or step functions.\nThe only demand is that the integral behaves well when a sequence of functions shrinks down to zero.\nFor example, the Riemann integral of continuous functions with compact support on the real line is such a starting point, and its extension is the Lebesgue integral.\n",
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