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  "body": "\n## Definition\n\nLet $\\Omega \\subseteq \\C^n$ be open, and let $d^c = i(\\bar\\partial - \\partial)$.\nLet $u$ be a locally bounded [[plurisubharmonic function|FF2P7ER3QT]] on $\\Omega$, and let $T$ be a closed [[positive current|BYJHP6A906]] of bidegree $(p, p)$ on $\\Omega$, with $p \\le n - 1$.\nThe coefficients of $T$ are measures and $u$ is locally bounded and Borel, so $uT$ is a well defined [[current|360H7MD9RD]].\nThe *Bedford–Taylor product* is the current\n$$dd^c u \\wedge T = dd^c (u T),$$\nwhere $dd^c$ is taken in the sense of currents.\nFor locally bounded plurisubharmonic functions $u_1, \\dots, u_k$ on $\\Omega$, with $k \\le n$, the product is defined by induction:\n$$dd^c u_1 \\wedge dd^c u_2 \\wedge \\cdots \\wedge dd^c u_k = dd^c \\left( u_1 \\, dd^c u_2 \\wedge \\cdots \\wedge dd^c u_k \\right).$$\nIn particular $(dd^c u)^n$ is the *Monge–Ampère measure* of $u$.\n\n## Remarks\n\nThe main facts of the theory are these.\nThe product $dd^c u \\wedge T$ is again a closed positive current, which makes the induction possible.\nWhen the $u_j$ are of class $C^2$ the product agrees with the wedge product of smooth forms, so $(dd^c u)^n$ agrees with the [[complex Monge–Ampère operator|MXRC891TQS]].\nIf $u_j^{(m)}$ decreases to $u_j$ as $m \\to \\infty$, for each $j$, then the products of the $u_j^{(m)}$ converge weakly to the product of the $u_j$.\nThe product is symmetric in $u_1, \\dots, u_k$.\nExample: for $n = 1$ and $T = 1$, $dd^c u = \\Delta u$ is the Riesz measure of the subharmonic function $u$, which is defined for every subharmonic $u$.\nNon-example: the definition does not apply to $u = \\log\\abs{z_1}$ on $\\C^2$, which is not locally bounded.\nFor unbounded plurisubharmonic functions in general, $(dd^c u)^n$ cannot be defined as a measure with good continuity properties.\n",
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