{"title":"表征某些函数族的博弈","authors":"Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca","doi":"10.1007/s00153-024-00922-9","DOIUrl":null,"url":null,"abstract":"<div><p>We obtain several game characterizations of Baire 1 functions between Polish spaces <i>X</i>, <i>Y</i> which extends the recent result of V. Kiss. Then we propose similar characterizations for equi-Bare 1 families of functions. Also, using related ideas, we give game characterizations of Baire measurable and Lebesgue measurable functions.</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 7-8","pages":"759 - 772"},"PeriodicalIF":0.3000,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Games characterizing certain families of functions\",\"authors\":\"Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca\",\"doi\":\"10.1007/s00153-024-00922-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We obtain several game characterizations of Baire 1 functions between Polish spaces <i>X</i>, <i>Y</i> which extends the recent result of V. Kiss. Then we propose similar characterizations for equi-Bare 1 families of functions. Also, using related ideas, we give game characterizations of Baire measurable and Lebesgue measurable functions.</p></div>\",\"PeriodicalId\":48853,\"journal\":{\"name\":\"Archive for Mathematical Logic\",\"volume\":\"63 7-8\",\"pages\":\"759 - 772\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2024-04-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive for Mathematical Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00153-024-00922-9\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00153-024-00922-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
引用次数: 0
摘要
我们得到了波兰空间 X、Y 之间 Baire 1 函数的几个博弈特征，这扩展了 V. Kiss 的最新成果。然后，我们为等贝叶 1 函数族提出了类似的特征。此外，我们还利用相关思想，给出了 Baire 可测函数和 Lebesgue 可测函数的博弈特征。
Games characterizing certain families of functions
We obtain several game characterizations of Baire 1 functions between Polish spaces X, Y which extends the recent result of V. Kiss. Then we propose similar characterizations for equi-Bare 1 families of functions. Also, using related ideas, we give game characterizations of Baire measurable and Lebesgue measurable functions.
期刊介绍：
The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.
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