{"id":246,"date":"2018-12-20T04:38:25","date_gmt":"2018-12-20T04:38:25","guid":{"rendered":"http:\/\/statp01.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=246"},"modified":"2018-12-20T04:39:43","modified_gmt":"2018-12-20T04:39:43","slug":"246","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/chapter\/246\/","title":{"rendered":"Set Functions"},"content":{"raw":"
<\/div>\r\n
<\/div>\r\n
\"epgp<\/a>\r\n<\/span><\/div>\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

Objectives<\/p>\r\n

I Measurable space<\/p>\r\n

Objectives<\/p>\r\n

I Measurable space\r\nI Set function<\/p>\r\n

Objectives<\/p>\r\n

I Measurable space\r\nI Set function\r\nI Additive an<\/p>\r\n

Objectives<\/p>\r\n

I Measurable space\r\nI Set function\r\nI Additive and \u03c3- additive set function\r\nI Measures<\/p>\r\n

Set function<\/p>\r\n

I Let \u2126 be the reference set and A be a class of subsets of R Set function\r\nI Let \u2126 be the reference set and A be a class of subsets of R\r\nI (\u2126, A): Measurable space<\/p>\r\n

I A set function \u03b3 on (\u2126, A) is an extended real valued function\r\ndefined on A i.e.<\/p>\r\n

Set function<\/p>\r\n

I Let \u2126 be the reference set and A be a class of subsets of R<\/p>\r\n

I (\u2126, A): Measurable space\r\nI A set function \u03b3 on (\u2126, A) is an extended real valued function\u00a0 defined on A i.e.\r\n\u03b3 : A \u2192 R? = [\u2212\u221e, \u221e]<\/p>\r\n

Set function<\/p>\r\n

I Let \u2126 be the reference set and A be a class of subsets of R<\/p>\r\n

I (\u2126, A): Measurable space<\/p>\r\n

I A set function \u03b3 on (\u2126, A) is an extended real valued function defined on A i.e.\r\n\u03b3 : A \u2192 R? = [\u2212\u221e, \u221e]<\/p>\r\n

I e.g. 1: \u2126 = {1, 2, 3, .....}, A = class of all subsets of \u2126<\/p>\r\n

\u03b3(A) = number of elements in A<\/p>\r\n

Let A = {1, 3, 5, 8, 9}, then \u03b3(A) = 5\r\nLet A = {1, 3, 5, 7, ....}, then \u03b3(A) = \u221e<\/p>\r\n

Set function<\/p>\r\n

I Let \u2126 be the reference set and A be a class of subsets of R\r\nI (\u2126, A): Measurable space\r\nI A set function \u03b3 on (\u2126, A) is an extended real valued function\r\ndefined on A i.e.\r\n\u03b3 : A \u2192 R? = [\u2212\u221e, \u221e]\r\nI e.g. 1: \u2126 = {1, 2, 3, .....}, A = class of all subsets of \u2126\r\n\u03b3(A) = number of elements in A\r\nLet A = {1, 3, 5, 8, 9}, then \u03b3(A) = 5\r\nLet A = {1, 3, 5, 7, ....}, then \u03b3(A) = \u221e\r\nI e.g. 2: \u2126 = R, A = class of all intervals of type\r\n(a, b]; \u2212\u221e \u2264 a < b \u2264 \u221e\r\n\u03b3(a, b] = b \u2212 a\r\nThen, \u03b3(1, 3] = 2, \u03b3(\u2212\u221e, 3] = \u221e<\/p>\r\n

Additive and \u03c3-additive set function\r\nI Additive:<\/p>\r\n

Additive and \u03c3-additive set function\r\nI Additive:<\/p>\r\n

A set function \u03b3 defined on (\u2126, A) is called additive if<\/p>\r\n

\"\"<\/p>\r\n

\"\"<\/p>\r\n

\"\"<\/p>\r\n

\"\"\"\"<\/p>\r\n

\"\"<\/p>\r\n

\"\"<\/p>\r\n\r\n\r\n\r\n\r\n
you can view video on Set Functions<\/strong><\/td>\r\n\"\"<\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>","rendered":"
<\/div>\n
<\/div>\n
\"epgp<\/a>
\n<\/span><\/div>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

Objectives<\/p>\n

I Measurable space<\/p>\n

Objectives<\/p>\n

I Measurable space
\nI Set function<\/p>\n

Objectives<\/p>\n

I Measurable space
\nI Set function
\nI Additive an<\/p>\n

Objectives<\/p>\n

I Measurable space
\nI Set function
\nI Additive and \u03c3- additive set function
\nI Measures<\/p>\n

Set function<\/p>\n

I Let \u2126 be the reference set and A be a class of subsets of R Set function
\nI Let \u2126 be the reference set and A be a class of subsets of R
\nI (\u2126, A): Measurable space<\/p>\n

I A set function \u03b3 on (\u2126, A) is an extended real valued function
\ndefined on A i.e.<\/p>\n

Set function<\/p>\n

I Let \u2126 be the reference set and A be a class of subsets of R<\/p>\n

I (\u2126, A): Measurable space
\nI A set function \u03b3 on (\u2126, A) is an extended real valued function\u00a0 defined on A i.e.
\n\u03b3 : A \u2192 R? = [\u2212\u221e, \u221e]<\/p>\n

Set function<\/p>\n

I Let \u2126 be the reference set and A be a class of subsets of R<\/p>\n

I (\u2126, A): Measurable space<\/p>\n

I A set function \u03b3 on (\u2126, A) is an extended real valued function defined on A i.e.
\n\u03b3 : A \u2192 R? = [\u2212\u221e, \u221e]<\/p>\n

I e.g. 1: \u2126 = {1, 2, 3, …..}, A = class of all subsets of \u2126<\/p>\n

\u03b3(A) = number of elements in A<\/p>\n

Let A = {1, 3, 5, 8, 9}, then \u03b3(A) = 5
\nLet A = {1, 3, 5, 7, ….}, then \u03b3(A) = \u221e<\/p>\n

Set function<\/p>\n

I Let \u2126 be the reference set and A be a class of subsets of R
\nI (\u2126, A): Measurable space
\nI A set function \u03b3 on (\u2126, A) is an extended real valued function
\ndefined on A i.e.
\n\u03b3 : A \u2192 R? = [\u2212\u221e, \u221e]
\nI e.g. 1: \u2126 = {1, 2, 3, …..}, A = class of all subsets of \u2126
\n\u03b3(A) = number of elements in A
\nLet A = {1, 3, 5, 8, 9}, then \u03b3(A) = 5
\nLet A = {1, 3, 5, 7, ….}, then \u03b3(A) = \u221e
\nI e.g. 2: \u2126 = R, A = class of all intervals of type
\n(a, b]; \u2212\u221e \u2264 a < b \u2264 \u221e
\n\u03b3(a, b] = b \u2212 a
\nThen, \u03b3(1, 3] = 2, \u03b3(\u2212\u221e, 3] = \u221e<\/p>\n

Additive and \u03c3-additive set function
\nI Additive:<\/p>\n

Additive and \u03c3-additive set function
\nI Additive:<\/p>\n

A set function \u03b3 defined on (\u2126, A) is called additive if<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n\n\n\n
you can view video on Set Functions<\/strong><\/td>\n\"\"<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"author":3,"menu_order":13,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["mr-samopriya-basu"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-246","chapter","type-chapter","status-publish","hentry","contributor-mr-samopriya-basu"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/246","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":4,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/246\/revisions"}],"predecessor-version":[{"id":257,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/246\/revisions\/257"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapters\/246\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/media?parent=246"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/pressbooks\/v2\/chapter-type?post=246"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/contributor?post=246"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp01\/wp-json\/wp\/v2\/license?post=246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}