Theory of Information and its Value by Ruslan L. Stratonovich & Roman V. Belavkin & Panos M. Pardalos & Jose C. Principe

Author:Ruslan L. Stratonovich & Roman V. Belavkin & Panos M. Pardalos & Jose C. Principe
Language: eng
Format: epub
ISBN: 9783030228330
Publisher: Springer International Publishing

(6.4.6)

(6.4.7)

These relations are analogous to formulae (6.2.4), (6.2.5) from the discrete version.

In the generalized case formulae (6.2.8), (6.2.7) take the form:

The other formulae from Sections 6.2 and 6.3 can be duplicated with no trouble. Henceforth, we write down the respective formulae in the required forms.

Satisfaction of the multiplicativity condition (6.4.1) for the normalized measure

means the equality

(6.4.8)

(see (1.​7.​16)). Therefore, we can use formula (1.​7.​17). Taking into account (1.​6.​17), (1.​7.​17) it is easy to see that formula (6.4.3) can be rewritten as follows

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