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  "body": "\n## Summary\n\nA Young measure on a set $\\Omega \\subseteq \\R^n$ is a measurable family $(\\nu_x)_{x \\in \\Omega}$ of [[probability measures|059TJN0NZ1]] on $\\R^m$.\nYoung measures describe the limits of oscillating sequences of functions: $\\nu_x$ is the distribution of the values that the functions take near $x$.\nThey let one pass to the limit in nonlinear expressions $\\varphi(u_k)$ when $u_k$ converges only weakly.\nThey are a standard tool in the calculus of variations and in nonlinear partial differential equations.\n\n## Explanations\n\n### L1 human\n\nTake the function on $(0,1)$ that jumps between $-1$ and $1$ on $k$ equal pieces, and let $k$ grow.\nThe functions oscillate faster and faster, and their weak limit is $0$.\nBut the square of each function is $1$, so the weak limit forgets something.\nThe Young measure keeps it: at every point it is the measure giving weight $1/2$ to $-1$ and $1/2$ to $1$.\nIt records which values occur and how often, not where they occur.\n",
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