{"id":60594,"date":"2025-06-18T11:00:25","date_gmt":"2025-06-18T10:00:25","guid":{"rendered":"https:\/\/www.istegroup.com\/?post_type=product&#038;p=60594"},"modified":"2025-12-15T15:15:57","modified_gmt":"2025-12-15T15:15:57","slug":"integration","status":"publish","type":"product","link":"https:\/\/www.istegroup.com\/en\/produit\/integration\/","title":{"rendered":"Int\u00e9gration"},"content":{"rendered":"<p>Cet ouvrage expose une th\u00e9orie simple et nouvelle de l\u2019int\u00e9gration, aussi bien r\u00e9elle que vectorielle, particuli\u00e8rement adapt\u00e9e \u00e0 l\u2019\u00e9tude des EDP. Cette th\u00e9orie permet d\u2019int\u00e9grer \u00e0 valeurs dans un espace E de Neumann, c\u2019est-\u00e0-dire dans lesquelles toutes suites de Cauchy convergent, ce qui englobe les espaces de Neumann et de Fr\u00e9chet, mais aussi les espaces \u00ab faibles \u00bb ou les espaces de distributions.<\/p>\n<p>Nous int\u00e9grons des \u00ab mesures int\u00e9grables \u00bb ce qui \u00e9quivaut aux \u00ab classes de fonctions int\u00e9grables p.p. \u00e9gales \u00bb lorsque E est un espace de Fr\u00e9chet. Plus pr\u00e9cis\u00e9ment, \u00e0 une classe f on associe la mesure <strong>f<\/strong>, o\u00f9 <strong>f<\/strong>(u) est l\u2019int\u00e9grale de fu pour toute fonction test u. L\u2019espace Lp(O;E) classique est l\u2019ensemble des f, et le n\u00f4tre est l\u2019ensemble des <strong>f <\/strong>; ces deux espaces sont isomorphes.<\/p>\n<p>Cet ouvrage \u00e9tudie en d\u00e9tail, pour tout espace de Neumann E, les propri\u00e9t\u00e9s de l\u2019int\u00e9grale et de Lp(O;E) : r\u00e9gularisation, image par une application lin\u00e9aire ou multilin\u00e9aire, changement de variable, s\u00e9paration de variables multiples, compacts et les duaux. Lorsque E est un espace de Fr\u00e9chet, nous \u00e9tudions l\u2019\u00e9quivalence des deux d\u00e9finitions et les propri\u00e9t\u00e9s li\u00e9es \u00e0 la convergence domin\u00e9e.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Cet ouvrage expose une th\u00e9orie simple et nouvelle de l\u2019int\u00e9gration, aussi bien r\u00e9elle que vectorielle, particuli\u00e8rement adapt\u00e9e \u00e0 l\u2019\u00e9tude des EDP. Cette th\u00e9orie permet d\u2019int\u00e9grer \u00e0 valeurs dans un espace E de Neumann, c\u2019est-\u00e0-dire dans lesquelles toutes suites de Cauchy convergent, ce qui englobe les espaces de Neumann et de Fr\u00e9chet, mais aussi les espaces [&hellip;]<\/p>\n","protected":false},"featured_media":60600,"template":"","meta":{"_acf_changed":false,"_links_to":"","_links_to_target":""},"product_brand":[],"product_cat":[671],"product_tag":[],"class_list":{"0":"post-60594","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-mathmatiques-et-statistiques-12506494","8":"first","9":"instock","10":"shipping-taxable","11":"purchasable","12":"product-type-variable"},"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Int\u00e9gration - ISTE Group<\/title>\n<meta name=\"description\" content=\"Cet ouvrage expose une th\u00e9orie simple et nouvelle de l\u2019int\u00e9gration, aussi bien r\u00e9elle que vectorielle, particuli\u00e8rement adapt\u00e9e \u00e0 l\u2019\u00e9tude des EDP.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.istegroup.com\/produit\/integration\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Int\u00e9gration - ISTE Group\" \/>\n<meta property=\"og:description\" content=\"Cet ouvrage expose une th\u00e9orie simple et nouvelle de l\u2019int\u00e9gration, aussi bien r\u00e9elle que vectorielle, particuli\u00e8rement adapt\u00e9e \u00e0 l\u2019\u00e9tude des EDP.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.istegroup.com\/produit\/integration\/\" \/>\n<meta property=\"og:site_name\" content=\"ISTE Group\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-15T15:15:57+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.istegroup.com\/wp-content\/uploads\/2025\/06\/030_Integration.png\" \/>\n\t<meta property=\"og:image:width\" content=\"553\" \/>\n\t<meta property=\"og:image:height\" content=\"834\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.istegroup.com\/produit\/integration\/\",\"url\":\"https:\/\/www.istegroup.com\/produit\/integration\/\",\"name\":\"Int\u00e9gration - ISTE Group\",\"isPartOf\":{\"@id\":\"https:\/\/www.istegroup.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.istegroup.com\/produit\/integration\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.istegroup.com\/produit\/integration\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.istegroup.com\/wp-content\/uploads\/2025\/06\/030_Integration.png\",\"datePublished\":\"2025-06-18T10:00:25+00:00\",\"dateModified\":\"2025-12-15T15:15:57+00:00\",\"description\":\"Cet ouvrage expose une th\u00e9orie simple et nouvelle de l\u2019int\u00e9gration, aussi bien r\u00e9elle que vectorielle, particuli\u00e8rement adapt\u00e9e \u00e0 l\u2019\u00e9tude des EDP.\",\"breadcrumb\":{\"@id\":\"https:\/\/www.istegroup.com\/produit\/integration\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.istegroup.com\/produit\/integration\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.istegroup.com\/produit\/integration\/#primaryimage\",\"url\":\"https:\/\/www.istegroup.com\/wp-content\/uploads\/2025\/06\/030_Integration.png\",\"contentUrl\":\"https:\/\/www.istegroup.com\/wp-content\/uploads\/2025\/06\/030_Integration.png\",\"width\":553,\"height\":834},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.istegroup.com\/produit\/integration\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.istegroup.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Shop\",\"item\":\"https:\/\/www.istegroup.com\/fr\/nouveautes\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Int\u00e9gration\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.istegroup.com\/#website\",\"url\":\"https:\/\/www.istegroup.com\/\",\"name\":\"ISTE Group\",\"description\":\"Publishing Knowledge\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.istegroup.com\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Int\u00e9gration - ISTE Group","description":"Cet ouvrage expose une th\u00e9orie simple et nouvelle de l\u2019int\u00e9gration, aussi bien r\u00e9elle que vectorielle, particuli\u00e8rement adapt\u00e9e \u00e0 l\u2019\u00e9tude des EDP.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.istegroup.com\/produit\/integration\/","og_locale":"en_US","og_type":"article","og_title":"Int\u00e9gration - ISTE Group","og_description":"Cet ouvrage expose une th\u00e9orie simple et nouvelle de l\u2019int\u00e9gration, aussi bien r\u00e9elle que vectorielle, particuli\u00e8rement adapt\u00e9e \u00e0 l\u2019\u00e9tude des EDP.","og_url":"https:\/\/www.istegroup.com\/produit\/integration\/","og_site_name":"ISTE Group","article_modified_time":"2025-12-15T15:15:57+00:00","og_image":[{"width":553,"height":834,"url":"https:\/\/www.istegroup.com\/wp-content\/uploads\/2025\/06\/030_Integration.png","type":"image\/png"}],"twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.istegroup.com\/produit\/integration\/","url":"https:\/\/www.istegroup.com\/produit\/integration\/","name":"Int\u00e9gration - ISTE Group","isPartOf":{"@id":"https:\/\/www.istegroup.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.istegroup.com\/produit\/integration\/#primaryimage"},"image":{"@id":"https:\/\/www.istegroup.com\/produit\/integration\/#primaryimage"},"thumbnailUrl":"https:\/\/www.istegroup.com\/wp-content\/uploads\/2025\/06\/030_Integration.png","datePublished":"2025-06-18T10:00:25+00:00","dateModified":"2025-12-15T15:15:57+00:00","description":"Cet ouvrage expose une th\u00e9orie simple et nouvelle de l\u2019int\u00e9gration, aussi bien r\u00e9elle que vectorielle, particuli\u00e8rement adapt\u00e9e \u00e0 l\u2019\u00e9tude des EDP.","breadcrumb":{"@id":"https:\/\/www.istegroup.com\/produit\/integration\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.istegroup.com\/produit\/integration\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.istegroup.com\/produit\/integration\/#primaryimage","url":"https:\/\/www.istegroup.com\/wp-content\/uploads\/2025\/06\/030_Integration.png","contentUrl":"https:\/\/www.istegroup.com\/wp-content\/uploads\/2025\/06\/030_Integration.png","width":553,"height":834},{"@type":"BreadcrumbList","@id":"https:\/\/www.istegroup.com\/produit\/integration\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.istegroup.com\/"},{"@type":"ListItem","position":2,"name":"Shop","item":"https:\/\/www.istegroup.com\/fr\/nouveautes\/"},{"@type":"ListItem","position":3,"name":"Int\u00e9gration"}]},{"@type":"WebSite","@id":"https:\/\/www.istegroup.com\/#website","url":"https:\/\/www.istegroup.com\/","name":"ISTE Group","description":"Publishing Knowledge","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.istegroup.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/www.istegroup.com\/en\/wp-json\/wp\/v2\/product\/60594","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.istegroup.com\/en\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/www.istegroup.com\/en\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.istegroup.com\/en\/wp-json\/wp\/v2\/media\/60600"}],"wp:attachment":[{"href":"https:\/\/www.istegroup.com\/en\/wp-json\/wp\/v2\/media?parent=60594"}],"wp:term":[{"taxonomy":"product_brand","embeddable":true,"href":"https:\/\/www.istegroup.com\/en\/wp-json\/wp\/v2\/product_brand?post=60594"},{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/www.istegroup.com\/en\/wp-json\/wp\/v2\/product_cat?post=60594"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/www.istegroup.com\/en\/wp-json\/wp\/v2\/product_tag?post=60594"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}