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| | + | <ref> [http://hea-www.harvard.edu/AstroStat http://hea-www.harvard.edu/AstroStat]; <nowiki> http://www.incagroup.org </nowiki>; <nowiki> http://astrostatistics.psu.edu </nowiki> </ref> |
| | + | |
| | + | ====Notes==== |
| | + | <references /> |
| | + | |
| | + | ------------------------------------------- |
| | | | |
| − | ====References====
| |
| | | | |
| | {| | | {| |
| − | |valign="top"|{{Ref|I}}|| Kiyosi Itô, "Introduction to probability theory", Cambridge (1984). {{MR|0777504}} {{ZBL|0545.60001}} | + | | A || B || C |
| − | |-
| |
| − | |valign="top"|{{Ref|Ru}}|| Thierry de la Rue, "Espaces de Lebesgue", ''Séminaire de Probabilités XXVII,'' Lecture Notes in Mathematics, '''1557''' (1993), Springer, Berlin, pp. 15–21. {{MR|1308547}} {{ZBL|0788.60001}}
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| | |- | | |- |
| − | |valign="top"|{{Ref|H}}|| Jean Haezendonck, "Abstract Lebesgue-Rohlin spaces", ''Bull. Soc. Math. de Belgique'' '''25''' (1973), 243–258. {{MR|0335733}} {{ZBL|0308.60006}} | + | | X || Y || Z |
| − | |-
| |
| − | |valign="top"|{{Ref|HN}}|| P.R. Halmos, J. von Neumann, "Operator methods in classical mechanics, II", ''Annals of Mathematics (2)'' '''43''' (1942), 332–350. {{MR|0006617}} {{ZBL|0063.01888}}
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| − | |-
| |
| − | |valign="top"|{{Ref|Ro}}|| V.A. Rokhlin, (1962), "On the fundamental ideas of measure theory", ''Translations (American Mathematical Society) Series 1,'' 10 (1962), 1–54. {{MR|0047744}} Translated from Russian: Рохлин, В. А. (1949), "Об основных понятиях теории меры", Математический Сборник (Новая Серия) 25(67): 107–150. {{MR|0030584}}
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| | |} | | |} |
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| | | | |
| − | {|
| + | |
| − | |valign="top"|{{Ref|P}}|| Karl Petersen, "Ergodic theory", Cambridge (1983). {{MR|0833286}} {{ZBL|0507.28010}}
| + | ----------------------------------------- |
| − | |-
| + | ----------------------------------------- |
| − | |valign="top"|{{Ref|H1}}|| P.R. Halmos, "Measure theory", Van Nostrand (1950). {{MR|0033869}} {{ZBL|0040.16802}}
| + | |
| − | |-
| + | $\newcommand*{\longhookrightarrow}{\lhook\joinrel\relbar\joinrel\rightarrow}$ |
| − | |valign="top"|{{Ref|H2}}|| P.R. Halmos, "Lectures on ergodic theory", Math. Soc. Japan (1956). {{MR|0097489}} {{ZBL|0073.09302}}
| + | |
| − | |-
| + | <asy> |
| − | |valign="top"|{{Ref|G}}|| Eli Glasner, "Ergodic theory via joinings", Amer. Math. Soc. (2003). {{MR|1958753}} {{ZBL|1038.37002}}
| + | size(100,100); |
| − | |-
| + | label(scale(1.7)*'$T(\\Sigma)\hookrightarrow T(\\Sigma,X)$',(0,0)); |
| − | |valign="top"|{{Ref|K}}|| Alexander S. Kechris, "Classical descriptive set theory", Springer-Verlag (1995). {{MR|1321597}} {{ZBL|0819.04002}}
| + | </asy> |
| − | |-
| + | |
| − | |valign="top"|{{Ref|F}}|| D.H. Fremlin, "Measure theory", Torres Fremlin, Colchester. Vol. 1: 2004 {{MR|2462519}} {{ZBL|1162.28001}}; Vol. 2: 2003 {{MR|2462280}} {{ZBL|1165.28001}}; Vol. 3: 2004 {{MR|2459668}} {{ZBL|1165.28002}}; Vol. 4: 2006 {{MR|2462372}} {{ZBL|1166.28001}}
| + | <asy> |
| − | |-
| + | size(220,220); |
| − | |valign="top"|{{Ref|S}}|| I.E. Segal, "Abstract probability spaces and a theorem of Kolmogoroff", ''Amer. J. Math.'' '''76''' (1954), 721–732. {{MR|0063602}} {{ZBL|0056.12301}}
| + | |
| − | |-
| + | import math; |
| − | |valign="top"|{{Ref|D}}|| L.E. Dubins, "Generalized random variables", ''Trans. Amer. Math. Soc.'' '''84''' (1957), 273–309. {{MR|0085326}} {{ZBL|0078.31003}}
| + | |
| − | |-
| + | int kmax=40; |
| − | |valign="top"|{{Ref|W}}|| David Williams, "Probability with martingales", Cambridge (1991). {{MR|1155402}} {{ZBL|0722.60001}}
| + | |
| − | |-
| + | guide g; |
| − | |valign="top"|{{Ref|C}}|| Constantin Carathėodory, "Die homomorphieen von Somen und die Multiplikation von Inhaltsfunktionen" (German), ''Annali della R. Scuola Normale Superiore di Pisa (Ser. 2)'' '''8''' (1939), 105–130. {{MR|1556820}} {{ZBL|0021.11403}}
| + | for (int k=-kmax; k<=kmax; ++k) { |
| − | |-
| + | real phi = 0.2*k*pi; |
| − | |valign="top"|{{Ref|HN}}|| P.R. Halmos, J. von Neumann, "Operator methods in classical mechanics, II", ''Annals of Mathematics (2)'' '''43''' (1942), 332–350. {{MR|0006617}} {{ZBL|0063.01888}}
| + | real rho = 1; |
| − | |}
| + | if (k!=0) { |
| | + | rho = sin(phi)/phi; |
| | + | } |
| | + | pair z=rho*expi(phi); |
| | + | g=g..z; |
| | + | } |
| | + | |
| | + | draw (g); |
| | + | |
| | + | defaultpen(0.75); |
| | + | draw ( (0,0)--(1.3,0), dotted, Arrow(SimpleHead,5) ); |
| | + | dot ( (1,0) ); |
| | + | label ( "$a$", (1,0), NE ); |
| | + | |
| | + | </asy> |
