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  "body": "\n## Summary\n\nThe harmonic measure of a domain, seen from a point $z$, is a probability measure on the boundary of the domain.\nIt is the measure that represents the value at $z$ of the solution of the [[Dirichlet problem|8D56GQ4AG8]] in terms of the boundary data.\nEquivalently, it is the distribution of the first exit point of a Brownian motion started at $z$.\nIt is invariant under conformal maps, and it is a central tool for estimating harmonic and holomorphic functions near the boundary.\n\n## Explanations\n\n### L1 human\n\nRelease a random walker at a point $z$ inside a region and wait until it first hits the boundary.\nThe harmonic measure of a piece of the boundary is the probability that the walker hits that piece first.\nParts of the boundary that are near $z$ and in the open get a large measure, while parts hidden deep inside narrow fjords get a small one.\nFor the centre of a disc, every arc of the circle gets a measure proportional to its length.\n",
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