{"id":34023,"date":"2021-03-11T00:00:02","date_gmt":"2021-03-11T00:00:02","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34023"},"modified":"2025-08-15T08:15:17","modified_gmt":"2025-08-15T08:15:17","slug":"cognosce-spatium-exemplorum-theoriae-probabilitatum","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/la\/cognosce-spatium-exemplorum-theoriae-probabilitatum\/","title":{"rendered":"Cognosce Spatium Exemplorum Theoriae Probabilitatum"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Cognosce Spatium Exemplorum Theoriae Probabilitatum<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>Summarium<\/strong><br \/><em>In hac lectione tractatur notio Spatii Probabilitatum, structura mathematica ex Spatio Exemplorum, Sigma-Algebra et Mensura Probabilitatis constituta. Accurate recensetur Spatium Exemplorum, intellectum ut congregatio omnium statuum possibilium cuiusdam processus fortuiti. Per exempla practica illustratur constructio spatii exemplorum discreti et continui, atque explicatur quomodo ex his efficiantur eventus mensurabiles et mensurae probabilitatis computentur. Haec lectio fundamentalis est ad intellegendum principia Theoriae Probabilitatum et ad fundamenta ponenda pro eius applicatione in diversis ambitibus.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>PROPOSITA DISCENDI:<\/strong><br \/>\nHis peractis lectionibus discipulus poterit:\n<\/p>\n<ol>\n<li><strong>Intellegere<\/strong> notionem Spatii Probabilitatum.<\/li>\n<li><strong>Ag\u00adnoscere<\/strong> elementa quae Spatium Probabilitatum constituunt.<\/li>\n<li><strong>Distinguere<\/strong> inter spatia exemplorum discreta et continua.<\/li>\n<li><strong>Construere<\/strong> spatia exemplorum discreta et continua.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>INDEX CONTENTORUM<\/strong><br \/>\n<a href=\"#1\">SPATIUM PROBABILITATUM<\/a><br \/>\n<a href=\"#2\">EXEMPLA SPATIORUM EXEMPLORUM<\/a><br \/>\n<a href=\"#3\">SPATIA EXEMPLORUM DISCRETA ET CONTINUA<\/a><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/NgYvWIWC_c4\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Spatium Probabilitatum<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=NgYvWIWC_c4&amp;t=89s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">Theoria Probabilitatum innititur obiecto quod Spatium Probabilitatum appellatur.<\/span><\/strong><\/a> Hoc est structura mathematica quae constat ex: (i) Spatio Exemplorum <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span>, (ii) Sigma-Algebra <span class=\"katex-eq\" data-katex-display=\"false\">\\Sigma<\/span> et (iii) Mensura Probabilitatis <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span>. Ad construendum spatium probabilitatum primum recognoscemus notionem <strong>spatii exemplorum.<\/strong><\/p>\n<p style=\"text-align: justify;\">Congregatio omnium <strong>statuum possibilium<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\omega<\/span> cuiusdam <strong><a href=\"https:\/\/toposuranos.com\/probabilidades-deterministas-indeterministas-azar\/\" rel=\"noopener\" target=\"_blank\">processus fortuiti<\/a><\/strong> constituit congeriem non vacuam <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega<\/span> quam <strong>Spatium Exemplorum<\/strong> appellamus.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Exempla Spatiorum Exemplorum<\/h2>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; background-color: #dddddd;\"><a href=\"https:\/\/www.youtube.com\/watch?v=NgYvWIWC_c4&amp;t=136s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">EXEMPLUM 1<\/span><\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify; background-color: #ffffff;\">Si nummum in a\u00ebra iaciamus, duo exitus possibiles habemus: Caput (C) et Cauda (S). Quare spatium exemplorum erit<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{1m}=\\{C,S\\}<\/span>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; background-color: #dddddd; color: #008000;\"><strong>EXEMPLUM 2<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify; background-color: #ffffff;\">Si experimentum prius iteretur, sed nunc cum duobus iactibus, tunc habebitur:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{2m}=\\{(C,C);(C,S);(S,C);(S,S)\\}<\/span>\n<p>Id est, omnes modi possibiles ordinandi capita et caudas in greges binos.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; background-color: #dddddd; color: #008000;\"><strong>EXEMPLUM 3<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify; background-color: #ffffff;\">Iactus aleae sex capitum spatium exemplorum habet sequentem formam:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{1d6}=\\{1,2,3,4,5,6\\}<\/span>\n<p>Id est, numerus in qualibet superficie eius indicatus.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; background-color: #dddddd; color: #008000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=NgYvWIWC_c4&amp;t=213s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">EXEMPLUM 4<\/span><\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify; background-color: #ffffff;\">Tempus vitae instrumenti electrici (mensum horis) spatium exemplorum habet huiusmodi:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_{ae}=\\{t\\in \\mathbb{R} \\;|\\; t\\geq 0\\}<\/span>\n<p>Id est, tempus vitae instrumenti est numerus <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span> contentus in intervallo <span class=\"katex-eq\" data-katex-display=\"false\"> [0,+\\infty[ <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Spatia Exemplorum Discreta et Continua<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=NgYvWIWC_c4&amp;t=285s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">Ex his exemplis possumus distinctionem facere inter duo genera spatiorum exemplorum,<\/span><\/strong><\/a> haec sunt discreta et continua. Spatia exemplorum discreta sunt illa quae, ut in tribus primis exemplis, ex congeriebus finitis constant, quamquam etiam infinita et numerabilia esse possunt (sicut quodlibet submultitudo <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{N}<\/span>). Contra, spatia exemplorum continua sunt congeriei infinitae et non numerabiles; plerumque repraesentantur per subintervalla <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span>.<\/p>\n<p style=\"text-align: justify;\">Ex elementis spatii exemplorum (statibus possibilibus) construuntur <strong>eventus mensurabiles<\/strong> (objecta sigma-algebrae) spatii probabilitatum, et super haec objecta computantur <strong>mensurae probabilitatis.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Cognosce Spatium Exemplorum Theoriae Probabilitatum SummariumIn hac lectione tractatur notio Spatii Probabilitatum, structura mathematica ex Spatio Exemplorum, Sigma-Algebra et Mensura Probabilitatis constituta. Accurate recensetur Spatium Exemplorum, intellectum ut congregatio omnium statuum possibilium cuiusdam processus fortuiti. Per exempla practica illustratur constructio spatii exemplorum discreti et continui, atque explicatur quomodo ex his efficiantur eventus mensurabiles et mensurae [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":25391,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":3,"footnotes":""},"categories":[1298,1364],"tags":[],"class_list":["post-34023","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematica","category-probabilitates-et-statistica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Cognosce Spatium Exemplorum Theoriae Probabilitatum - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Cognosce omnia singularia Spatii Exemplorum quae fortasse nesciebas et te para ad progrediendum in theoria probabilitatum.\" \/>\n<meta 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