On Four Approaches to Density

Name: On Four Approaches to Density
Brand: Peter Lang Gmbh, Internationaler Verlag Der W
SKU: 9783631649411
Price: 2195.0 INR
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ISBN13: 9783631649411
Binding: Hardcover
Subject: N/A
Publisher: Peter Lang Gmbh, Internationaler Verlag Der W
Publisher Imprint: Peter Lang Gmbh, Internationaler Verlag Der W
Publication Date: June 13, 2014
Pages: 97
Original Price: GBP 20.9
Language: English
Edition: New ed
Item Weight: 316 grams
BISAC Subject(s): Probability & Statistics / General

About The Book

The aim of this short book is to present the elements of a systematic theory of certain types of finitely additive probability measures on a set of positive integers. The conventional name of this measures is density with an adjective. Every set of positive integers is finite or infinite countable. It is, thus, impossible to consider a sigma additive probability measure defined on a certain class of the sets of positive integers, which could distinguish between the finite and infinite sets of positive integers. The greatness of the first is negligible. From the point of view of cardinality, the second has the same greatness. If we want to consider the measure of greatness, which could divide the sets of positive integers from a certain aspect of their structure, it is more convenient to consider the finitely additive measure. We shall study four most known types of these set functions. One of the important rules in the set of positive integers is played by the relation to divisibility, thus our main attention is devoted to the connection between density and this relation. We try to derive some known results from the basic definitions.

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