Certain games, category, and measure

Slawomir Solecki

doi:10.1090/S0002-9939-1993-1149979-X

Certain games, category, and measure

Slawomir Solecki

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For A ⊂ 2^ω and X ⊂ ω consider an infinite game Г(A, X) in which two players I and II choose c_n ϵ (0,1). c_n is chosen by I if n ϵ X and by II if n ϵ ω\X. I wins if (c₀, c₁, c₂,…) ϵ A. We analyze connections between A and the family of all sets X ⊂ ω for which I has a winning strategy in Г(A, X). Certain similarities and differences appear if one formulates these connections in the language of category and of Lebesgue measure.

Original language	English (US)
Pages (from-to)	275-279
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	119
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1993-1149979-X
State	Published - Sep 1993

Keywords

Categor
Infinite games
Measure

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Online availability

10.1090/S0002-9939-1993-1149979-X

Library availability

Discover UIUC Full Text

Cite this

@article{6c3bd82cb93845c69668acdc139fdbc5,

title = "Certain games, category, and measure",

abstract = "For A ⊂ 2ω and X ⊂ ω consider an infinite game Г(A, X) in which two players I and II choose cn ϵ (0,1). cn is chosen by I if n ϵ X and by II if n ϵ ω\X. I wins if (c0, c1, c2,…) ϵ A. We analyze connections between A and the family of all sets X ⊂ ω for which I has a winning strategy in Г(A, X). Certain similarities and differences appear if one formulates these connections in the language of category and of Lebesgue measure.",

keywords = "Categor, Infinite games, Measure",

author = "Slawomir Solecki",

year = "1993",

month = sep,

doi = "10.1090/S0002-9939-1993-1149979-X",

language = "English (US)",

volume = "119",

pages = "275--279",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - Certain games, category, and measure

AU - Solecki, Slawomir

PY - 1993/9

Y1 - 1993/9

N2 - For A ⊂ 2ω and X ⊂ ω consider an infinite game Г(A, X) in which two players I and II choose cn ϵ (0,1). cn is chosen by I if n ϵ X and by II if n ϵ ω\X. I wins if (c0, c1, c2,…) ϵ A. We analyze connections between A and the family of all sets X ⊂ ω for which I has a winning strategy in Г(A, X). Certain similarities and differences appear if one formulates these connections in the language of category and of Lebesgue measure.

AB - For A ⊂ 2ω and X ⊂ ω consider an infinite game Г(A, X) in which two players I and II choose cn ϵ (0,1). cn is chosen by I if n ϵ X and by II if n ϵ ω\X. I wins if (c0, c1, c2,…) ϵ A. We analyze connections between A and the family of all sets X ⊂ ω for which I has a winning strategy in Г(A, X). Certain similarities and differences appear if one formulates these connections in the language of category and of Lebesgue measure.

KW - Categor

KW - Infinite games

KW - Measure

UR - http://www.scopus.com/inward/record.url?scp=84966206714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966206714&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1993-1149979-X

DO - 10.1090/S0002-9939-1993-1149979-X

M3 - Article

AN - SCOPUS:84966206714

SN - 0002-9939

VL - 119

SP - 275

EP - 279

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

Certain games, category, and measure

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this