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  "body": "\n## Summary\n\nA locally compact abelian group, or LCA group, is a commutative topological group whose topology is Hausdorff and locally compact.\nThese groups are the natural setting of Fourier analysis.\nEach LCA group has a Haar measure and a dual group of characters, and Pontryagin duality says that the group is recovered from its dual.\n\n## Explanations\n\n### L1 human\n\nThink of a group where you can add elements, the order does not matter, and there is a notion of nearness with small compact neighbourhoods.\nThe real line $\\R$ with addition is the basic picture: every point has a closed bounded interval around it.\nThe integers $\\Z$ with the discrete topology, the circle group and every finite abelian group are also examples.\nOn all of these, one can integrate and expand functions into waves, just as Fourier series expand functions on the circle.\n",
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