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  "body": "\n## Summary\n\nA positive harmonic function is a [[harmonic function|0DEB0JMN0W]] that takes only positive values on its domain.\nPositivity is a strong constraint: on a connected open set, the values of such a function at two points control each other, by [[Harnack's inequality|YNH832D50W]].\nOn the unit disc and on balls, positive harmonic functions are exactly the Poisson integrals of nonzero positive finite Borel measures on the boundary sphere.\nThey are the starting point of the theory of the Martin boundary.\n\n## Explanations\n\n### L1 human\n\nThink of a steady temperature distribution that is above zero everywhere in a room.\nSuch a temperature cannot be very large at one point and very small at a nearby point.\nFor example, on the half-plane $y \u003e 0$ the function $u(x, y) = y$ is harmonic and positive.\nOn the unit disc, the [[Poisson kernel|TCYSWCTYYM]] $(1 - \\abs{z}^2)/\\abs{1 - z}^2$ is another example.\n",
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