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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}}>}}

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 | first1=J.Laurie | title=讣告：journal 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>}}

===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===