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Area Digital technology – Fundamental concepts / Information theory

IEV ref171-07-14

Symbol
I(x)

en
information content
quantitative measure of information about the occurrence of an event x of definite probability p(x), equal to the logarithm of the reciprocal of this probability

I(x)=log 1 p(x) =logp(x) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGjbGaaiikaiaadIhacaGGPaGaeyypa0tcLbuaciGGSbGaai4B aiaacEgakmaalaaabaqcLbuacaaIXaaakeaacaWGWbGaaiikaiaadI hacaGGPaaaaiabg2da9iabgkHiTKqzafGaciiBaiaac+gacaGGNbGc caWGWbGaaiikaiaadIhacaGGPaaaaa@5250@

EXAMPLE Let { a,b,c } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aaomaacmaakeaajugibiaadggacaGGSaGaamOyaiaacYcacaWGJbaa kiaawUhacaGL9baaaaa@43FE@ be a set of three events and let p(a)=0,5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadggacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaiwdaaaa@43D9@ , p(b)=0,25 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadkgacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaikdacaaI1aaaaa@4496@ and p(c)=0,25 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadogacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaikdacaaI1aaaaa@4497@ be the probabilities of their occurrences. The information contents of these events are: I(a)=lb 1 0,50 Sh=1Sh MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aajugibiaadMeacaGGOaGaamyyaiaacMcajugabiabg2da9iaacYga caGGIbGcdaWcaaqaaKqzaeGaaGymaaGcbaqcLbqacaaIWaGaaiilai aaiwdacaaIWaaaaiaacofacaGGObGaeyypa0JaaGymaiaaysW7caGG tbGaaiiAaaaa@4F62@ , I(b)=lb 1 0,25 Sh=2Sh MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aajugibiaadMeacaGGOaGaamOyaiaacMcajugabiabg2da9iaacYga caGGIbGcdaWcaaqaaKqzaeGaaGymaaGcbaqcLbqacaaIWaGaaiilai aaikdacaaI1aaaaiaacofacaGGObGaeyypa0JaaGOmaiaaysW7caGG tbGaaiiAaaaa@4F66@ , I(c)=lb 1 0,25 Sh=2Sh MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aajugibiaadMeacaGGOaGaam4yaiaacMcajugabiabg2da9iaacYga caGGIbGcdaWcaaqaaKqzaeGaaGymaaGcbaqcLbqacaaIWaGaaiilai aaikdacaaI1aaaaiaacofacaGGObGaeyypa0JaaGOmaiaaysW7caGG tbGaaiiAaaaa@4F67@ .

Note 1 to entry: For a set of equiprobable events, the information content of each event is equal to the decision content of the set.


[SOURCE: IEC 80000-13:2008, 13-24, modified – Addition of information useful for the context of the IEV, and adaptation to the IEV rules]


fr
quantité d’information, f
mesure quantitative de l'information concernant la réalisation d'un événement x de probabilité déterminée p(x), égale au logarithme de l'inverse de cette probabilité

I(x)=log 1 p(x) =logp(x) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGjbGaaiikaiaadIhacaGGPaGaeyypa0tcLbuaciGGSbGaai4B aiaacEgakmaalaaabaqcLbuacaaIXaaakeaacaWGWbGaaiikaiaadI hacaGGPaaaaiabg2da9iabgkHiTKqzafGaciiBaiaac+gacaGGNbGc caWGWbGaaiikaiaadIhacaGGPaaaaa@5250@

EXEMPLE: Soit { a,b,c } MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aaomaacmaakeaajugibiaadggacaGGSaGaamOyaiaacYcacaWGJbaa kiaawUhacaGL9baaaaa@43FE@ un jeu de trois événements dont les probabilités de réalisation sont p(a)=0,5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadggacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaiwdaaaa@43D9@ , p(b)=0,25 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadkgacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaikdacaaI1aaaaa@4496@ et p(c)=0,25 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aacaWGWbGaaiikaiaadogacaGGPaqcLbqacqGH9aqpcaaIWaGaaiil aiaaikdacaaI1aaaaa@4497@ . Les quantités d'information de ces événements sont: I(a)=lb 1 0,50 Sh=1Sh MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aajugibiaadMeacaGGOaGaamyyaiaacMcajugabiabg2da9iaacYga caGGIbGcdaWcaaqaaKqzaeGaaGymaaGcbaqcLbqacaaIWaGaaiilai aaiwdacaaIWaaaaiaacofacaGGObGaeyypa0JaaGymaiaaysW7caGG tbGaaiiAaaaa@4F62@ , I(b)=lb 1 0,25 Sh=2Sh MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aajugibiaadMeacaGGOaGaamOyaiaacMcajugabiabg2da9iaacYga caGGIbGcdaWcaaqaaKqzaeGaaGymaaGcbaqcLbqacaaIWaGaaiilai aaikdacaaI1aaaaiaacofacaGGObGaeyypa0JaaGOmaiaaysW7caGG tbGaaiiAaaaa@4F66@ , I(c)=lb 1 0,25 Sh=2Sh MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaiGc9aspC0FXdbbc9asFfpec8Eeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmaadiWaaiWabaabaiaafaaake aajugibiaadMeacaGGOaGaam4yaiaacMcajugabiabg2da9iaacYga caGGIbGcdaWcaaqaaKqzaeGaaGymaaGcbaqcLbqacaaIWaGaaiilai aaikdacaaI1aaaaiaacofacaGGObGaeyypa0JaaGOmaiaaysW7caGG tbGaaiiAaaaa@4F67@ .

Note 1 à l’article: Pour un ensemble d'événements équiprobables, la quantité d'information de chaque événement est égale à la quantité de décision de l'ensemble.


[SOURCE: IEC 80000-13:2008, 13-24, modifié – Ajout d’informations utiles pour le contexte de l’IEV, et adaptation aux règles de l’IEV]


ar
محتوى المعلومات

de
Informationsgehalt, m

fi
informaatiomäärä

ja
情報量

pl
zawartość informacji, f

pt
quantidade de informação

zh
信息内容

Publication date: 2019-03-29
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