Word.ws English Dictionary

π-system

π-system noun: a non-empty collection of subsets of a given set Ώ that is closed under non-empty finite intersections.

Noun

π-system (plural π-systems)

  1. A non-empty collection of subsets of a given set Ώ that is closed under non-empty finite intersections.
    • To see this, first check that #92;sigma(X#95;0,X#95;1,#92;dots)#61;#92;sigma(#92;mathcalF#95;0), where #92;textstyle#92;mathcalF#95;0#58;#61;#92;bigcup#92;infty#95;#123;k#61;0#125;#92;sigma(X#95;0,#92;dots,X#95;k) is a field and, in particular, a #92;boldsymbol#92;pi-system.2007, Rabi Bhattacharya, Edward C. Waymire, A Basic Course in Probability Theory, Springer, page 49
    • We start with a basis of simple roots #92;Delta of #92;Phi. Then we apply all possible elementary transformations and add the resulting #92;boldsymbol#92;pi-systems to the list. Of course, if #92;Gamma is a #92;boldsymbol#92;pi-system, and #92;Gamma' is a #92;boldsymbol#92;pi-system obtained from...2017, Willem Adriaan de Graaf, Computation with Linear Algebraic Groups, Taylor & Francis (CRC Press), page 221

Forms of π-system

pluralπ-systems
alternative formpi-system

Questions about π-system

What does π-system mean?
Π-system means a non-empty collection of subsets of a given set Ώ that is closed under non-empty finite intersections.
What part of speech is π-system?
Π-system is a noun.
What is the plural of π-system?
The plural of π-system is π-systems.

Words near π-system in the dictionary

  1. π bonds
  2. π Day
  3. π-mer
  4. π-mers
  5. π-on
  6. π-system
  7. π-systems
  8. πon
  9. σ-additivity
  10. σ-algebra
  11. σ-algebras

Source and license

Adapted from Wiktionary: π-system (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “π-system.” Word.ws, https://word.ws/%CF%80-system. Based on Wiktionary, CC BY-SA 4.0.