{
  "aliases": [
    "sigma-field"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "04WSW8T3SY"
    },
    {
      "field": "specializes",
      "target": "0WQXY32Q8D"
    },
    {
      "field": "specializes",
      "target": "6HVCTJGB61"
    },
    {
      "field": "uses",
      "target": "130FCDWRT1"
    },
    {
      "field": "uses",
      "target": "2T33SA540E"
    },
    {
      "field": "uses",
      "target": "8SFZYANHNC"
    },
    {
      "field": "uses",
      "target": "AAT8PVDW23"
    },
    {
      "field": "uses",
      "target": "BBHM1A36M7"
    },
    {
      "field": "uses",
      "target": "CFQXJ4FHR4"
    },
    {
      "field": "uses",
      "target": "FN2WRRF6V9"
    },
    {
      "field": "uses",
      "target": "M8X6VZD91K"
    },
    {
      "field": "uses",
      "target": "Q8EXG7EKYW"
    },
    {
      "field": "uses",
      "target": "RDE658H8Z4"
    },
    {
      "field": "uses",
      "target": "W01FD2A8NK"
    },
    {
      "field": "about",
      "target": "2T33SA540E"
    }
  ],
  "body": "\n## Summary\n\nA σ-algebra on a set is a family of subsets that contains the whole set and is closed under complements and countable unions.\nIn probability theory, the σ-algebra is the family of events, the sets to which we give a probability. The node [[sigma-algebra|04WSW8T3SY]] gives the precise definition.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "aliases": [
      "sigma-field"
    ],
    "kind": "concept",
    "msc": [
      "28A05"
    ],
    "name": "Sigma-algebra",
    "same_as": {
      "wikidata": "Q217357",
      "wikipedia": "Σ-algebra"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Σ-algebra"
      }
    ],
    "tag": "0SV8K0TDGY"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0SV8K0TDGY/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/0SV8K0TDGY.md",
  "msc": [
    "28A05"
  ],
  "name": "Sigma-algebra",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0SV/0SV8K0TDGY.md",
  "status": null,
  "tag": "0SV8K0TDGY",
  "uri": "m2://0SV8K0TDGY",
  "url": "https://tamnd.github.io/math2/wiki/sigma-algebra/",
  "writing": {
    "tag": "0SV8K0TDGY",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      }
    ]
  }
}
