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Article #74

Re: Entoropy

#74
From: sakaguchi fuminori
Date: Fri, 13 Mar 1998 00:00
25 lines
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ๅ‚ๅฃใจ็”ณใ—ใพใ™ใ€‚ๆ–‡็Œฎใฎ็ดนไป‹ใงใฏใชใ„ใฎใงใ™ใŒใƒปใƒปใƒป

From article <6e888o$h3g$1@ripspost.aist.go.jp>
	by "Kazuya Takabatake" <takahata@cniri.go.jp>

> ็ขบ็އๅค‰ๆ•ฐX_1,...,X_nใŒใ‚ใ‚‹ใจใA,Bใ‚’ใ“ใ‚Œใ‚‰ใฎ็ขบ็އๅค‰ๆ•ฐใฎไปปๆ„ใฎ็ต„ใจใ™ใ‚‹ใจๅŒๆ™‚ใ‚จ
> ใƒณใƒˆใƒญใƒ”ใƒผHใซใคใ„ใฆ
> 
> ใ€€H(A)>=0
> ใ€€H(A)<=H(AB)<=H(A)+H(B)
> 
> ใŒๆˆ็ซ‹ใคใ“ใจใฏๅˆ็ญ‰็š„ใช่จผๆ˜Žใ‹ใ‚‰ๅพ—ใ‚‰ใ‚Œใพใ™ใŒ๏ผŒ้€†ใซไธŠใฎๆกไปถใ‚’ๆบ€ใŸใ™Hใ‚’ไธŽใˆใŸ
> ใจใ๏ผŒใใ‚Œใ‚’ๅŒๆ™‚ใ‚จใƒณใƒˆใƒญใƒ”ใƒผใซๆŒใค็ขบ็އๅค‰ๆ•ฐX_1,...,X_nใฏๅญ˜ๅœจใ™ใ‚‹ใงใ—ใ‚‡ใ†ใ‹?
> (ใคใพใ‚ŠๅŒๆ™‚็ขบ็އใŒๅญ˜ๅœจใ™ใ‚‹ใ‹?)

H(AB)=H(A) ใจใชใ‚‹ใฎใฏใ€B ใŒ A ใ‹ใ‚‰ใฟใฆ deterministic ใชๅ ดๅˆใซ
้™ใ‚‰ใ‚Œใพใ™ใ‹ใ‚‰ใ€H(A)>=H(B) ใฎๅ ดๅˆใซ้™ใ‚‰ใ‚Œใพใ™ใ€‚ใ—ใŸใŒใฃใฆใ€
H(A)=H(AB)<2H(A)<H(A)+H(B) ใฎๅ ดๅˆใฏๅญ˜ๅœจใ—ใชใ„ใจๆ€ใ„ใพใ™ใ€‚

๏ผƒใใ‚Œใ‹ใ‚‰ใ€n ใŒๆœ€ๅˆใ‹ใ‚‰ fix ใ•ใ‚Œใฆใ„ใ‚‹ใ‹ใ„ใชใ„ใ‹ใงใ‚‚ใ€
  ๅ•้กŒใฏๅค‰ใ‚ใฃใฆใใ‚‹ใจๆ€ใ„ใพใ™ใ€‚
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                                         saka@dignet.fuee.fukui-u.ac.jp
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From: c54262@sakura.kudpc.kyoto-u.ac.jp (sakaguchi fuminori)
Subject: Re: Entoropy
Date: 1998/03/13
Message-ID: <6eacg3$4f0@sakura.kudpc.kyoto-u.ac.jp>
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Organization: Data Processing Center, Kyoto University. Kyoto, Japan.
Newsgroups: fj.comp.theory,fj.sci.informatics,fj.sci.math