{"id":14736,"date":"2022-09-21T06:41:47","date_gmt":"2022-09-21T06:41:47","guid":{"rendered":"https:\/\/file.currentschoolnews.com\/?post_type=product&p=14736"},"modified":"2022-09-21T15:58:52","modified_gmt":"2022-09-21T15:58:52","slug":"integration-in-lattice-spaces","status":"publish","type":"product","link":"https:\/\/pastexamquestions.com\/product\/integration-in-lattice-spaces\/","title":{"rendered":"Integration\u00a0in Lattice Spaces"},"content":{"rendered":"

– Integration\u00a0in Lattice Spaces –<\/strong><\/span><\/p>\n

Download Integration\u00a0in Lattice Spaces<\/strong><\/span>. Students who are writing their projects can get this material to aid their research work.<\/span><\/span><\/p>\n

Abstract<\/strong><\/h3>\n

The goal of this thesis is to extend the notion of integration with respect to a measure to Lattice spaces. To do so the paper is first summarizing the notion of integration with respect to a measure on R. <\/span><\/p>\n

Then, a construction of an integral on Banach spaces called the Bochner integral is introduced and the main focus which is integration on lattice spaces is lastly addressed.<\/span>\u00a0<\/span><\/p>\n

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Introduction<\/strong><\/h3>\n

1.1 Background of the Study<\/strong><\/p>\n

Integration is a mathematical technique used to find areas, volumes and so many other mathematical measures. But to make the notion of integration easy to picture, we define it simply as a mean to find area under the curve of a function; and the result of the integration is called the integral of the function.<\/span><\/p>\n

Therefore, it is not a surprise that, there are different types of integration, since the functions to be integrated have variety of properties.<\/span><\/p>\n

The first type of integration that comes to our mind, when we talk about area under a curve is the Riemann integration named as Riemann-<\/span>Stieltjes<\/span>\u00a0integration under its general form. <\/span><\/p>\n

However, we will see that, this integration is applicable to real-valued functions and requires some specific properties that all real-valued functions need not have. <\/span><\/p>\n

Therefore, we will introduce another type of integration, called the Lebesgue-<\/span>Stieltjes<\/span>\u00a0integration, that will address most of the limits of the Riemann-<\/span>Stieltjes<\/span>\u00a0Integration. <\/span><\/p>\n

The Lebesgue –<\/span>Stieltjes<\/span>\u00a0integration gives us a mean to compute the integral of a large range of real-valued function with an undeniable property called measurability. So, the Lebesgue-<\/span>Stieljes<\/span>\u00a0Integration is addressed as the integration of real-valued measurable mappings with respect to a\u00a0\u2018measure\u2019. <\/span><\/p>\n

While the Riemann-<\/span>Stieljes<\/span> integration focus on powerful computation tools, the Lebesgue <\/span>Stieljes<\/span>\u00a0theory\u00a0<\/span>adresses<\/span>\u00a0powerful results of existence, limits theory, integration and differentiation under the integral sign. As such, it is unavoidable in modern analysis. <\/span><\/p>\n

Now, the goal of this thesis is not only to expand the integration of\u00a0<\/span>realvalued<\/span> measurable mappings to Banach spaces but also to introduce the notion of integration of measurable mappings with values in Lattice spaces.<\/span>\u00a0<\/span><\/p>\n

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