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Kolmogorov integral
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Kolmogorov integral (or Kolmogoroff integral) is a generalized integral introduced by <a href="/facts/Andrey_Kolmogorov/bEKwtrs6">Kolmogoroff</a> (1930) including the <a href="/facts/Lebesgue%25E2%2580%2593Stieltjes_integral/W4GD5Tlr">Lebesgue–Stieltjes integral</a>, the <a href="/facts/Burkill_integral/7WUr6jNU">Burkill integral</a>, and the <a href="/facts/Hellinger_integral/rnN7YuaK">Hellinger integral</a> as special cases. The integral is a limit over a directed family of partitions, when the resulting limiting value is independent of the tags of each partition segment. </p> <ul><li><a href="https://dml.cz/dmlcz/102009">"On integration in Banach spaces, VI"</a>, Ivan Dobrakov and Pedro Morales, <i>Czechoslovak Mathematical Journal,</i> 35 (1985), #2, 173-187, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.21136%2FCMJ.1985.102009">10.21136/CMJ.1985.102009</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a><a href="https://mathscinet.ams.org/mathscinet-getitem?mr=787123">787123</a>.</li> <li><a href="https://dml.cz/dmlcz/102239">"On integration in Banach spaces, VII"</a>, Ivan Dobrakov, <i>Czechoslovak Mathematical Journal</i>, 38 (1988), #3, 434-449, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.21136%2FCMJ.1988.102239">10.21136/CMJ.1988.102239</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a><a href="https://mathscinet.ams.org/mathscinet-getitem?mr=950297">950297</a>.</li> <li><a href="/facts/Andrey_Kolmogorov/bEKwtrs6">Kolmogoroff, A.</a> (1930), "Untersuchungen über den Integralbegriff", <i><a href="/facts/Mathematische_Annalen/GPhGaonc">Mathematische Annalen</a></i>, 103 (1): 654–696, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2FBF01455714">10.1007/BF01455714</a>, <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0025-5831">0025-5831</a></li> <li>Skvortsov, V. A. (2001) [1994], <a href="https://www.encyclopediaofmath.org/index.php?title=Kolmogorov_integral">"Kolmogorov integral"</a>, <i><a href="/facts/Encyclopedia_of_Mathematics/WC6mGtPm">Encyclopedia of Mathematics</a></i>, <a href="/facts/European_Mathematical_Society/B3h7b672">EMS Press</a></li></ul>