更改

In 1920s fundamental contributions to probability theory were made in the Soviet Union by mathematicians such as [[Sergei Bernstein]], [[Aleksandr Khinchin]],{{efn|The name Khinchin is also written in (or transliterated into) English as Khintchine.<ref name="Doob1934">{{cite journal|last1=Doob|first1=Joseph|title=Stochastic Processes and Statistics|journal=Proceedings of the National Academy of Sciences of the United States of America|volume=20|issue=6|year=1934|pages=376–379|doi=10.1073/pnas.20.6.376|pmid=16587907|pmc=1076423|bibcode=1934PNAS...20..376D}}</ref>}} and [[Andrei Kolmogorov]].<ref name="Cramer1976"/> Kolmogorov published in 1929 his first attempt at presenting a mathematical foundation, based on measure theory, for probability theory.<ref name="KendallBatchelor1990page33">{{cite journal|last1=Kendall|first1=D. G.|last2=Batchelor|first2=G. K.|last3=Bingham|first3=N. H.|last4=Hayman|first4=W. K.|last5=Hyland|first5=J. M. E.|last6=Lorentz|first6=G. G.|last7=Moffatt|first7=H. K.|last8=Parry|first8=W.|last9=Razborov|first9=A. A.|last10=Robinson|first10=C. A.|last11=Whittle|first11=P.|title=Andrei Nikolaevich Kolmogorov (1903–1987)|journal=Bulletin of the London Mathematical Society|volume=22|issue=1|year=1990|page=33|issn=0024-6093|doi=10.1112/blms/22.1.31}}</ref> In the early 1930s Khinchin and Kolmogorov set up probability seminars, which were attended by researchers such as [[Eugene Slutsky]] and [[Nikolai Smirnov (mathematician)|Nikolai Smirnov]],<ref name="Vere-Jones2006page1">{{cite book|last1=Vere-Jones|first1=David|title=Encyclopedia of Statistical Sciences|chapter=Khinchin, Aleksandr Yakovlevich|page=1|year=2006|doi=10.1002/0471667196.ess6027.pub2|isbn=978-0471667193}}</ref> and Khinchin gave the first mathematical definition of a stochastic process as a set of random variables indexed by the real line.<ref name="Doob1934"/><ref name="Vere-Jones2006page4">{{cite book|last1=Vere-Jones|first1=David|title=Encyclopedia of Statistical Sciences|chapter=Khinchin, Aleksandr Yakovlevich|page=4|year=2006|doi=10.1002/0471667196.ess6027.pub2|isbn=978-0471667193}}</ref>{{efn|Doob, when citing Khinchin, uses the term 'chance variable', which used to be an alternative term for 'random variable'.<ref name="Snell2005">{{cite journal|last1=Snell|first1=J. Laurie|title=Obituary: Joseph Leonard Doob|journal=Journal of Applied Probability|volume=42|issue=1|year=2005|page=251|issn=0021-9002|doi=10.1239/jap/1110381384|doi-access=free}}</ref> }}

In 1920s fundamental contributions to probability theory were made in the Soviet Union by mathematicians such as [[Sergei Bernstein]], [[Aleksandr Khinchin]],{{efn|The name Khinchin is also written in (or transliterated into) English as Khintchine.<ref name="Doob1934">{{cite journal|last1=Doob|first1=Joseph|title=Stochastic Processes and Statistics|journal=Proceedings of the National Academy of Sciences of the United States of America|volume=20|issue=6|year=1934|pages=376–379|doi=10.1073/pnas.20.6.376|pmid=16587907|pmc=1076423|bibcode=1934PNAS...20..376D}}</ref>}} and [[Andrei Kolmogorov]].<ref name="Cramer1976"/> Kolmogorov published in 1929 his first attempt at presenting a mathematical foundation, based on measure theory, for probability theory.<ref name="KendallBatchelor1990page33">{{cite journal|last1=Kendall|first1=D. G.|last2=Batchelor|first2=G. K.|last3=Bingham|first3=N. H.|last4=Hayman|first4=W. K.|last5=Hyland|first5=J. M. E.|last6=Lorentz|first6=G. G.|last7=Moffatt|first7=H. K.|last8=Parry|first8=W.|last9=Razborov|first9=A. A.|last10=Robinson|first10=C. A.|last11=Whittle|first11=P.|title=Andrei Nikolaevich Kolmogorov (1903–1987)|journal=Bulletin of the London Mathematical Society|volume=22|issue=1|year=1990|page=33|issn=0024-6093|doi=10.1112/blms/22.1.31}}</ref> In the early 1930s Khinchin and Kolmogorov set up probability seminars, which were attended by researchers such as [[Eugene Slutsky]] and [[Nikolai Smirnov (mathematician)|Nikolai Smirnov]],<ref name="Vere-Jones2006page1">{{cite book|last1=Vere-Jones|first1=David|title=Encyclopedia of Statistical Sciences|chapter=Khinchin, Aleksandr Yakovlevich|page=1|year=2006|doi=10.1002/0471667196.ess6027.pub2|isbn=978-0471667193}}</ref> and Khinchin gave the first mathematical definition of a stochastic process as a set of random variables indexed by the real line.<ref name="Doob1934"/><ref name="Vere-Jones2006page4">{{cite book|last1=Vere-Jones|first1=David|title=Encyclopedia of Statistical Sciences|chapter=Khinchin, Aleksandr Yakovlevich|page=4|year=2006|doi=10.1002/0471667196.ess6027.pub2|isbn=978-0471667193}}</ref>{{efn|Doob, when citing Khinchin, uses the term 'chance variable', which used to be an alternative term for 'random variable'.<ref name="Snell2005">{{cite journal|last1=Snell|first1=J. Laurie|title=Obituary: Joseph Leonard Doob|journal=Journal of Applied Probability|volume=42|issue=1|year=2005|page=251|issn=0021-9002|doi=10.1239/jap/1110381384|doi-access=free}}</ref> }}

20世纪20年代，苏联的数学家们对概率论做出了重大贡献，比如[[Sergei Bernstein]]，[[Aleksandr Khinchin]]，{{efn | Khinchin这个名字也用英语写成（或音译成）Khintchine。<ref name=“Doob1934”>{cite journal | last1=Doob | first1=Joseph | title=随机过程与统计| journal=美国国家科学院学报美国体积＝20π＝6π＝376×379π＝10.1073 /PNAS 20.637 6pMID＝16587907πPMC＝1076423 BiBCODE＝1934 PNAS…20 .37 6D } </REF> }和[[Andrei Kolmogorov ] ] < 1929】命名为“CRAME1976”/Kolmogorov于1984年发表了基于测量理论的数学基础的首次尝试。概率论的概率论。<ref name=“KendallBatchelo1990 Page33”>{〈引用期刊| last1=Kendall | first1=D.G.| last2=Batchelor | first2=G.K.| last3=Bingham | first3=N.H.| last4=Hayman | first4=W.K.| last5=Hyland | first5=第一5=J.M.M.E.|124;最后6=洛伦兹|第一6=G.G.最后7=最后7=最后7=最后7=N.H.莫法特| first7=H.K.| last8=Parry | first8=W.| last9=Razborov | first9=A.A.| last10=Robinson | first10=C。A、 最后11=Whittle；first11=P.；title=AndreiNikolaevich Kolmogorov（1903-1987年）| journal=伦敦数学社会公报| volume=22 | issue=1 | year=1990年| page=33 | issn=0024-6093；doi=10.1112/blms/22.1.31}</ref>在20世纪30年代初，胡仁钦和科尔莫戈罗夫在20世纪30年代初建立了概率研讨会，这些研讨会由研究者参加，如[[Eugene Slutsky]]]等[Eugene Slutsky]等[Eugene Slutsky Slutsky slut在[和[[尼古拉斯米尔诺夫（数学家）尼古拉斯米尔诺夫（数学家）尼古拉斯米尔诺夫]]，<ref name=“Vere-Jones2006page1”>{引用书| last1=Vere Jones；first1=David；title=统计科学百科全书|第章=章呼仁钦，Aleksandr yakovovlevich；page=1 |年=2006年124; doi=10.1002/0471667196.ess6027/076027 667196.ess6027.pub2 | isbn=978-0471667193}|第978-0471667193}}第}</ref>和钦钦给出了随机过程将随机过程作为一组随机变量的一组随机变量按实线编入索引。<ref name=“Doob1934”/>><ref name=“Vere-Jones2006page4”>{{cite book | last1=Vere Jones | first1=David | title=统计科学百科全书|第124;章章章=Khinchin，Aleksandr yakovolevicch | page=4 | year=2006年124; doi=10.1002/0471667196.ess6027/677196.ess6027.pub2 | isbn=978-0471667193}| 978-0471}</ref>{efn|嘟嘟，引用钦钦时，使用了“机会变量”这个词，以前是“随机变量”的替代名词。<ref name=“Snell2005”>{{{cite journal | last1=Snell | first 1=J.Laurie；title=讣告：Joseph Leonard Doob | journal=journal of Applied Probability；volume=42；issue=1 | year=2005年2005年| page=251 | issn=0021-9002 | doi=10.1239/jap/1110381384 | doi access=free}}</ref ref</ref ref</ref}}>}}

20世纪20年代，苏联的数学家们对概率论做出了重大贡献，比如[[Sergei Bernstein]]，[[Aleksandr Khinchin]]，{{efn | Khinchin这个名字也用英语写成（或音译成）Khintchine。<ref name=“Doob1934”>{cite journal | last1=Doob | first1=Joseph | title=随机过程与统计| journal=美国国家科学院学报美国体积＝20π＝6π＝376×379π＝10.1073 /PNAS 20.637 6pMID＝16587907πPMC＝1076423 BiBCODE＝1934 PNAS…20 .37 6D } </REF> }和[[Andrei Kolmogorov ] ] < 1929】命名为“CRAME1976”/Kolmogorov于1984年发表了基于测量理论的数学基础的首次尝试。概率论的概率论。<ref name=“KendallBatchelo1990 Page33”>{〈引用期刊| last1=Kendall | first1=D.G.| last2=Batchelor | first2=G.K.| last3=Bingham | first3=N.H.| last4=Hayman | first4=W.K.| last5=Hyland | first5=第一5=J.M.M.E.|124;最后6=洛伦兹|第一6=G.G.最后7=最后7=最后7=最后7=N.H.莫法特| first7=H.K.| last8=Parry | first8=W.| last9=Razborov | first9=A.A.| last10=Robinson | first10=C。A、 最后11=Whittle；first11=P.；title=AndreiNikolaevich Kolmogorov（1903-1987年）| journal=伦敦数学社会公报| volume=22 | issue=1 | year=1990年| page=33 | issn=0024-6093；doi=10.1112/blms/22.1.31}</ref>在20世纪30年代初，胡仁钦和科尔莫戈罗夫在20世纪30年代初建立了概率研讨会，这些研讨会由研究者参加，如[[Eugene Slutsky]]]等和[[尼古拉·斯米尔诺夫（数学家）|尼古拉·斯米尔诺夫]]，<ref name=“Vere-Jones2006page1”>{cite book | last1=Vere Jones | first1=David | title=统计科学百科全书| chapter=Khinchin，Aleksandr Yakovlevich | page=1 | year=2006 | doi=10.1002/0471667196.ess6027.pub2 | isbn=978-0471667193}}</ref>还有金钦给出了第一个随机变量的数学定义，把随机过程作为以实数线索引的一组随机变量。<ref name=“Doob1934”/><ref name=“Vere-Jones2006page4”>{cite book | last1=Vere Jones | first1=David | title=统计科学百科全书| chapter=Khinchin，Aleksandr Yakovlevich | page=4 | year=2006 | doi=10.1002/0471667196.ess6027.pub2 | isbn=978-0471667193}}</ref>{{efn | Doob在引用Khinchin时，使用了“机会变量”这个词，它曾经是“随机变量”的替代词。<ref name=“Snell2005”>{{{cite journal | last1=Snell | first 1=J.Laurie；title=讣告：Joseph Leonard Doob | journal=journal of Applied Probability；volume=42；issue=1 | year=2005年2005年| page=251 | issn=0021-9002 | doi=10.1239/jap/1110381384 | doi access=free}}</ref ref</ref ref</ref}}>}}

===Birth of modern probability theory现代概率论的诞生===

===Birth of modern probability theory现代概率论的诞生===