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  "body": "\n## Summary\n\nA sequence $(f_n)$ of [[measurable functions|YYNCJSR0PJ]] converges in measure to $f$ if bad sets shrink.\nFor each $\\varepsilon \u003e 0$, the set where $f_n$ differs from $f$ by at least $\\varepsilon$ must have measure tending to $0$.\nIt is weaker than uniform convergence and than convergence in $L^p$.\nIn probability theory it is called convergence in probability.\n\n## Explanations\n\n### L1 human\n\nConvergence in measure does not ask the functions to approach $f$ at every point.\nIt asks that the region where $f_n$ is far from $f$ shrinks to size $0$.\nFor example, a narrow bump of height $1$ that sweeps again and again across $[0, 1]$, getting narrower each pass, converges to $0$ in measure.\nYet at each point the bump returns infinitely often, so the sequence converges at no point.\n",
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