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  "body": "\n## Summary\n\nBedford–Taylor theory defines the [[complex Monge–Ampère operator|MXRC891TQS]] $(dd^c u)^n$ for plurisubharmonic functions $u$ that are only locally bounded, not differentiable.\nThe products $dd^c u_1 \\wedge \\cdots \\wedge dd^c u_k$ are defined inductively as closed [[positive currents|BYJHP6A906]], and they are continuous along decreasing sequences of plurisubharmonic functions.\nEric Bedford and B. A. Taylor developed the theory in work published in 1976 and 1982.\nIt gives the Monge–Ampère capacity and solves the Dirichlet problem for the complex Monge–Ampère equation with continuous data on strongly pseudoconvex domains.\nIt is the starting point of modern pluripotential theory.\n\n## Explanations\n\n### L1 human\n\nFor a smooth function the Monge–Ampère operator is a determinant of second derivatives, but many important plurisubharmonic functions are not smooth.\nFor example, $\\max(\\log\\abs{z_1}, \\log\\abs{z_2}, 0)$ is continuous and plurisubharmonic on $\\C^2$, but it has corners.\nBedford and Taylor showed how to give a meaning to the Monge–Ampère measure of such functions by using derivatives in the sense of distributions, one factor at a time.\nFor the function above, the Monge–Ampère measure turns out to be a constant multiple of the uniform measure on the torus $\\abs{z_1} = \\abs{z_2} = 1$.\n",
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