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  "body": "\n## Summary\n\nAn integral current is a [[current|360H7MD9RD]] that behaves like an oriented surface with integer multiplicities.\nIt is given by integration over a [[rectifiable set|7N0GFMW05R]] with an orientation and a positive integer multiplicity.\nBoth it and its boundary have finite mass.\nIntegral currents include all compact oriented smooth submanifolds with boundary.\nBy the [[Federer–Fleming compactness theorem|TPXYARH912]], they are closed under the limits that matter for area minimisation.\nThey are the setting of the Plateau problem in all dimensions and codimensions.\n\n## Explanations\n\n### L1 human\n\nAn integral current is a generalised surface that can have corners and singularities, and parts counted twice or three times, but never a fractional number of times.\nYou integrate a differential form over it as over an ordinary oriented surface, counting each part with its multiplicity.\nFor example, the unit disc in the plane, traversed once, is an integral $2$-current with boundary the unit circle.\nThe same disc counted twice is also one, but the disc counted half a time is not.\n",
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