The Springer International Series in Engineering and Computer Science

# The Mathematical Theory of Information

Authors: Kåhre, Jan

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The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon's noisy channel. The entropy in the 'classical information theory' is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron's law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making 'two plus two greater than four'. Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation.

Pages 1-21

Kåhre, Jan

• The Law of Diminishing Information

Pages 22-40

Kåhre, Jan

• General Properties of Information

Pages 41-79

Kåhre, Jan

• Specific Information Measures

Pages 80-115

Kåhre, Jan

• Selected Applications

Pages 116-144

Kåhre, Jan

eBook 64,19 €
price for Spain (gross)
• ISBN 978-1-4615-0975-2
• Digitally watermarked, DRM-free
• Included format: PDF
• ebooks can be used on all reading devices
Hardcover 93,59 €
price for Spain (gross)
• ISBN 978-1-4020-7064-8
• Free shipping for individuals worldwide
• Institutional customers should get in touch with their account manager
• Covid-19 shipping restrictions
• Usually ready to be dispatched within 3 to 5 business days, if in stock
• The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 77,99 €
price for Spain (gross)
• ISBN 978-1-4613-5332-4
• Free shipping for individuals worldwide
• Institutional customers should get in touch with their account manager
• Covid-19 shipping restrictions
• Usually ready to be dispatched within 3 to 5 business days, if in stock
• The final prices may differ from the prices shown due to specifics of VAT rules

## Bibliographic Information

Bibliographic Information
Book Title
The Mathematical Theory of Information
Authors
Series Title
The Springer International Series in Engineering and Computer Science
Series Volume
684
2002
Publisher
Springer US
eBook ISBN
978-1-4615-0975-2
DOI
10.1007/978-1-4615-0975-2
Hardcover ISBN
978-1-4020-7064-8
Softcover ISBN
978-1-4613-5332-4
Series ISSN
0893-3405
Edition Number
1
Number of Pages
XIV, 502
Topics