{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "YMGHNBDZCP"
    }
  ],
  "body": "\n## Summary\n\nThe oscillation of a function at a point measures the size of the spread of its values near that point.\nIt is $0$ exactly at the points where the function is [[continuous|0EEE2CZB2A]], so it measures how badly continuity fails.\nIt is a basic tool in the study of the set of discontinuities, for example in [[Lebesgue's criterion for Riemann integrability|0565EGK6XP]].\n\n## Explanations\n\n### L1 human\n\nLook at the values of a function on a small window around a point, and measure the gap between the largest and the smallest of them.\nShrink the window and see what this gap tends to.\nThat limit is the oscillation at the point.\nFor the sign function, the values near $0$ are $-1$, $0$ and $1$, so the oscillation at $0$ is $2$.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "26A15"
    ],
    "name": "Oscillation of a function",
    "same_as": {
      "wikidata": "Q7106411",
      "wikipedia": "Oscillation (mathematics)"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Oscillation_(mathematics)"
      }
    ],
    "tag": "5XW4N8KY3Y"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/5XW4N8KY3Y/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/5XW4N8KY3Y.md",
  "msc": [
    "26A15"
  ],
  "name": "Oscillation of a function",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/5XW/5XW4N8KY3Y.md",
  "status": null,
  "tag": "5XW4N8KY3Y",
  "uri": "m2://5XW4N8KY3Y",
  "url": "https://math2.tamnd.com/wiki/oscillation-of-a-function/",
  "writing": {
    "tag": "5XW4N8KY3Y",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}