Information measures: information and its description in science and engineering
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [.a.]
Springer
2001
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 547 S. graph. Darst. |
| ISBN: | 3540416331 |
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MARC
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| 084 | |a SK 830 |0 (DE-625)143259: |2 rvk | ||
| 084 | |a 11 |2 ssgn | ||
| 100 | 1 | |a Arndt, Christoph |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Information measures |b information and its description in science and engineering |c C. Arndt |
| 264 | 1 | |a Berlin [.a.] |b Springer |c 2001 | |
| 300 | |a XIX, 547 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Informationsmaß - Informationstheorie | |
| 650 | 4 | |a Informationstheorie - Entropie | |
| 650 | 0 | 7 | |a Entropie |0 (DE-588)4014894-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Informationstheorie |0 (DE-588)4026927-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Informationsmaß |0 (DE-588)4330787-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Entropie |0 (DE-588)4014894-4 |D s |
| 689 | 0 | 1 | |a Informationstheorie |0 (DE-588)4026927-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Informationsmaß |0 (DE-588)4330787-5 |D s |
| 689 | 1 | 1 | |a Informationstheorie |0 (DE-588)4026927-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009294393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009294393 | |
Record in the Search Index
| _version_ | 1807772589948403712 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
SYMBOLS,
EXPRESSIONS
AND
ABBREVIATIONS
.
XVII
ABSTRACT
.
1
STRUCTURE
AND
STRUCTURING
.
3
1
INTRODUCTION
.
7
SCIENCE
AND
INFORMATION
.
8
MAN
AS
CONTROL
LOOP
.
13
INFORMATION,
COMPLEXITY
AND
TYPICAL
SEQUENCES
.
14
CONCEPTS
OF
INFORMATION
.
15
INFORMATION,
ITS
TECHNICAL
DIMENSION
AND
THE
MEANING
OF
A
MESSAGE
16
INFORMATION
AS
A
CENTRAL
CONCEPT?
.
18
2
BASIC
CONSIDERATIONS
.
23
2.1
FORMAL
DERIVATION
OF
INFORMATION
.
23
2.1.1
UNIT
AND
REFERENCE
SCALE
.
28
2.1.2
INFORMATION
AND
THE
UNIT
ELEMENT
.
30
2.2
APPLICATION
OF
THE
INFORMATION
MEASURE
(SHANNON
'
S
INFORMATION)
.
31
2.2.1
SUMMARY
.
39
2.3
THE
LAW
OF
WEBER
AND
FECHNER
.
42
2.4
INFORMATION
OF
DISCRETE
RANDOM
VARIABLES
.
44
3
HISTORIC
DEVELOPMENT
OF
INFORMATION
THEORY
.
47
3.1
DEVELOPMENT
OF
INFORMATION
TRANSMISSION
.
47
3.1.1
SAMUEL
F.
B.
MORSE
1837
.
47
3.1.2
THOMAS
EDISON
1874
.
47
3.1.3
NYQUIST
1924
.
48
3.1.4
OPTIMAL
NUMBER
OF
CHARACTERS
OF
THE
ALPHABET
USED
FOR
THE
CODING
49
3.2
DEVELOPMENT
OF
INFORMATION
FUNCTIONS
.
51
3.2.1
HARTLEY
1928
.
51
3.2.2
DENNIS
GABOR
1946
.
52
3.2.3
SHANNON
1948
.
53
3.2.3.1
VALIDITY
OF
THE
POSTULATES
FOR
SHANNON
'
S
INFORMATION
.
57
3.2.3.2
SHANNON
'
S
INFORMATION
(ANOTHER
POSSIBILITY
OF
A
DERIVATION)
.59
XII
TABLE
OF
CONTENTS
3.2.3.3
PROPERTIES
OF
SHANNON
'
S
INFORMATION,
ENTROPY
.
61
3.2.3.4
SHANNON
'
S
ENTROPY
OR
SHANNON
'
S
INFORMATION?
.
66
3.2.3.5
THE
KRAFT
INEQUALITY
.
67
KRAFT
'
S
INEQUALITY:
.
67
PROOF
OF
KRAFT
'
S
INEQUALITY:
.
68
3.2.3.6
LIMITS
OF
THE
OPTIMAL
LENGTH
OF
CODEWORDS
.
75
3.2.3.6.1
SHANNON
'
S
CODING
THEOREM
.
75
3.2.3.6.2
A
SEQUENCE
OF
N
SYMBOLS
(ELEMENTS)
.
76
3.2.3.6.3
APPLICATION
OF
THE
PREVIOUS
RESULTS
.
79
3.2.3.7
INFORMATION
AND
UTILITY
(CODING,
PORFOLIO
ANALYSIS)
.
82
4
THE
CONCEPT
OF
ENTROPY
IN
PHYSICS
.
85
THE
LAWS
OF
THERMODYNAMICS:
.
85
4.1
MACROSCOPIC
ENTROPY
.
86
4.1.1
SADI
CARNOT
1824
.
86
4.1.2
CLAUSIUS
'
S
ENTROPY
1850
.
86
4.1.3
INCREASE
OF
ENTROPY
IN
A
CLOSED
SYSTEM
.
87
4.1.4
PRIGOGINE
'
S
ENTROPY
.
88
4.1.5
ENTROPY
BALANCE
EQUATION
.
89
4.1.6
GIBBS
'
S
FREE
ENERGY
AND
THE
QUALITY
OF
THE
ENERGY
.
90
4.1.7
CONSIDERATIONS
ON
THE
MACROSCOPIC
ENTROPY
.
91
4.1.7.1
IRREVERSIBLE
TRANSFORMATIONS
.
92
4.1.7.2
PERPETUUM
MOBILE
AND
TRANSFER
OF
HEAT
.
93
4.2
STATISTICAL
ENTROPY
.
94
4.2.1
BOLTZMANN
'
S
ENTROPY
.
94
4.2.2
DERIVATION
OF
BOLTZMANN
'
S
ENTROPY
.
95
4.2.2.1
VARIATION,
PERMUTATION
AND
THE
FORMULA
OF
STIRLING.
95
4.2.2.2
SPECIAL
CASE:
TWO
STATES
.
100
4.2.2.3
EXAMPLE:
LOTTERY
.
101
4.2.3
THE
BOLTZMANN
FACTOR
.
102
4.2.4
MAXIMUM
ENTROPY
IN
EQUILIBRIUM
.
106
4.2.5
STATISTICAL
INTERPRETATION
OF
ENTROPY
.
112
4.2.6
EXAMPLES
REGARDING
STATISTICAL
ENTROPY
.
113
4.2.6.1
ENERGY
AND
FLUCTUATION
.
115
4.2.6.2
QUANTIZED
OSCILLATOR
.
116
4.2.7
BRILLOUIN-SCHRODINGER
NEGENTROPY
.
120
4.2.7.1
BRILLOUIN:
PRECISE
DEFINITION
OF
INFORMATION
.
121
4.2.7.2
NEGENTROPY
AS
A
GENERALIZATION
OF
CARNOT
'
S
PRINCIPLE
.
124
MAXWELL
'
S
DEMON
.
125
4.2.8
INFORMATION
MEASURES
OF
HARTLEY
AND
BOLTZMANN
.
126
4.2.8.1
EXAMPLES
.
128
4.2.9
SHANNON
'
S
ENTROPY
.
128
4.3
DYNAMIC
ENTROPY
.
130
4.3.1
EDDINGTON
AND
THE
ARROW
OF
TIME
.
130
4.3.2
KOLMOGOROV
'
S
ENTROPY
.
131
TABLE
OF
CONTENTS
XIII
4.3.3
RENYI
'
S
ENTROPY
.
132
5
EXTENSION
OF
SHANNON
'
S
INFORMATION
.
133
5.1
RENYI
'
S
INFORMATION
1960
.
133
5.1.1
PROPERTIES
OF
RENYI
'
S
ENTROPY
.
137
5.1.2
LIMITS
IN
THE
INTERVAL
0
A
.
140
5.1.3
NONNEGATIVITY
FOR
DISCRETE
EVENTS
.
143
5.1.4
ADDITIVITY
AND
A
CONNECTION
TO
MINKOWSKI
'
S
NORM
.
145
5.1.5
THE
MEANING
OF
S
R
/A)
FOR
A
1
AND
A
1:
.
147
5.1.6
GRAPHICAL
PRESENTATIONS
OF
RENYI
'
S
INFORMATION
.
155
5.2
ANOTHER
GENERALIZED
ENTROPY
(LOGICAL
EXPANSION)
.
156
5.3
GAIN
OF
INFORMATION
VIA
CONDITIONAL
PROBABILITIES
.
162
5.4
OTHER
ENTROPY
OR
INFORMATION
MEASURES
.
173
5.4.1
DAROCZY
'
S
ENTROPY
.
173
5.4.2
QUADRATIC
ENTROPY
.
174
5.4.3
R-NORM
ENTROPY
.
176
6
GENERALIZED
ENTROPY
MEASURES
.
179
6.1
THE
CORRESPONDING
MEASURES
OF
DIVERGENCE
.
189
6.2
WEIGHTED
ENTROPIES
AND
EXPECTATION
VALUES
OF
ENTROPIES
.
193
7
INFORMATION
FUNCTIONS
AND
GAUSSIAN
DISTRIBUTIONS
.
197
7.1
RENYI
'
S
INFORMATION
OF
A
GAUSSIAN
DISTRIBUTED
RANDOM
VARIABLE
.
197
7.1.1
RENYI
'
S
A-INFORMATION
.
198
7.1.2
RENYI
'
S
G-DIVERGENCE
.
200
7.2
SHANNON
'
S
INFORMATION
.
204
8
SHANNON
'
S
INFORMATION
OF
DISCRETE
PROBABILITY
DISTRIBUTIONS
.
207
8.1
CONTINUOUS
AND
DISCRETE
RANDOM
VARIABLES
.
209
8.1.1
SUMMARY
.
212
8.2
SHANNON
'
S
INFORMATION
OF
A
GAUSSIAN
DISTRIBUTION
.
213
8.3
SHANNON
'
S
INFORMATION
AS
THE
POSSIBLE
GAIN
OF
INFORMATION
IN
AN
OBSERVATION
.
217
8.4
LIMITS
OF
THE
INFORMATION,
LIMITATIONS
OF
THE
RESOLUTION
.
219
8.4.1
THE
RESOLUTION
OR
THE
PRECISION
OF
THE
MEASUREMENTS
.
219
8.4.2
THE
UNCERTAINTY
RELATION
OF
THE
FOURIER
TRANSFORMATION
.
221
8.5
MAXIMIZATION
OF
THE
ENTROPY
OF
A
CONTINUOUS
RANDOM
VARIABLE
.
222
9
INFORMATION
FUNCTIONS
FOR
GAUSSIAN
DISTRIBUTIONS
PART
II
.227
9.1
KULLBACK
'
S
INFORMATION
.
227
9.1.1
GI
FOR
GAUSSIAN
DISTRIBUTION
DENSITES
.
230
XIV
TABLE
OF
CONTENTS
9.2
KULLBACK
'
S
DIVERGENCE
.
237
9.2.1
JENSEN
'
S
INEQUALITY
FOR
GI
.
238
9.3
KOLMOGOROV
'
S
INFORMATION
.
239
9.4
TRANSFORMATION
OF
THE
COORDINATE
SYSTEM
AND
THE
EFFECTS
ON
THE
INFORMATION
.
246
9.4.1
SO-INFORMATION
.
247
9.4.2
G-DIVERGENCE
.
249
9.4.3
S-INFORMATION
.
250
9.4.3.1
EXAMPLE
.
251
9.4.4
DISCRIMINATION
INFORMATION
.
252
9.4.5
KOLMOGOROV
'
S
INFORMATION
.
253
9.4.6
PREREQUISITES
FOR
THE
TRANSFORMATIONS
.
255
9.5
TRANSFORMATION,
DISCRETE
AND
CONTINUOUS
MEASURES
OF
ENTROPY
.
255
9.6
SUMMARY
OF
THE
INFORMATION
FUNCTIONS
.
257
10
BOUNDS
OF
THE
VARIANCE
.
261
10.1
CRAMER-RAO
BOUND
.
262
10.1.1
FISHER
'
S
INFORMATION
FOR
GAUSSIAN
DISTRIBUTION
DENSITIES
.
265
10.1.2
FISHER
'
S
INFORMATION
AND
KULLBACK
'
S
INFORMATION
.
268
10.1.3
FISHER
'
S
INFORMATION
AND
THE
METRIC
TENSOR
.
273
10.1.4
FISHER
'
S
INFORMATION
AND
THE
STOCHASTIC
OBSERVABILITY
.
274
10.1.4.1
FISHER
'
S
INFORMATION
AND
THE
MATRIX-RICCATI
EQUATION
.
276
10.1.5
FISHER
'
S
INFORMATION
AND
MAXIMUM
LIKELIHOOD
ESTIMATION.
279
10.1.6
FISHER
'
S
INFORMATION
AND
WEIGHTED
LEAST-SQUARES
ESTIMATION
.
282
10.1.7
THE
AVAILABILITY
OF
THE
CRAMER-RAO
BOUND
.
284
10.1.8
EFFICIENCY,
ASYMPTOTIC
EFFICIENCY,
CONSISTENCY,
BIAS
.
287
10.1.8.1
UNBIASED
ESTIMATOR
.
287
10.1.8.2
CONSISTENCY
.
287
10.1.8.3
EFFICIENCY.
288
10.1.9
SUMMARY
.
289
10.2
CHAPMAN-ROBBINS
BOUND
.
289
10.2.1
CRAMER-RAO
BOUND
VERSUS
CHAPMAN-ROBBINS
BOUND
.
293
10.3
BHATTACHARRYA
BOUND
.
294
REMARK:
.
298
REMARK
.
302
10.3.1
BHATTACHARRYA
BOUND
AND
CRAMER-RAO
BOUND
.
302
10.3.2
BHATTACHARRYA
'
S
BOUND
FOR
GAUSSIAN
DISTRIBUTION
DENSITIES
.
304
10.4
BARANKIN
BOUND
.
307
10.5
OTHER
BOUNDS
.
312
FRASER-GUTTMAN
BOUND
.
313
KIEFER
BOUND
.
313
EXTENDED
FRASER-GUTTMAN
BOUND
.
314
10.6
SUMMARY
.
315
10.7
BIASED
ESTIMATOR
.
316
10.7.1
BIASED
ESTIMATOR
VERSUS
UNBIASED
ESTIMATOR
.
321
TABLE
OF
CONTENTS
XV
11
AMBIGUITY
FUNCTION
.
327
11.1
THE
AMBIGUITY
FUNCTION
AND
KULLBACK
'
S
INFORMATION
.
332
11.2
CONNECTION
BETWEEN
AMBIGUITY
FUNCTION
AND
FISHER
'
S
INFORMATION
.333
11.3
MAXIMUM
LIKELIHOOD
ESTIMATION
AND
THE
AMBIGUITY
FUNCTION
.
334
11.3.1
MAXIMUM
LIKELIHOOD
ESTIMATION
=
MINIMUM
KULLBACK
ESTIMATION
=
MAXIMUM
AMBIGUITY
ESTIMATION
=
MINIMUM
VARIANCE
ESTIMATION.
334
11.3.2
MAXIMUM
LIKELIHOOD
ESTIMATION
.
336
11.3.2.1
APPLICATION:
DISCRIMINATOR
(DEMODULATION)
.
336
11.4
THE
ML
ESTIMATION
IS
ASYMPTOTICALLY
EFFICIENT
.
340
11.5
TRANSITION
TO
THE
AKAIKE
INFORMATION
CRITERION
.
344
12
AKAIKE
'
S
INFORMATION
CRITERION
.
347
12.1
AKAIKE
'
S
INFORMATION
CRITERION
AND
REGRESSION
.
347
12.1.1
LEAST-SQUARES
REGRESSION
.
347
12.1.2
APPLICATION
OF
THE
RESULTS
TO
THE
AMBIGUITY
FUNCTION
.
351
12.2
BIC,
SC
OR
HQ
.
356
13
CHANNEL
INFORMATION
.
363
13.1
REDUNDANCY
.
370
13.1.1
KNOWLEDGE,
REDUNDANCY,
UTILITY
.
374
13.2
RATE
OF
TRANSMISSION
AND
EQUIVOCATION
.
375
13.3
HADAMARD
'
S
INEQUALITY
AND
GIBBS
'
S
SECOND
THEOREM
.
377
13.4
KOLMOGOROV
'
S
INFORMATION
.
379
13.5
KULLBACKS
DIVERGENCE
.
382
13.6
AN
EXAMPLE
OF
A
TRANSMISSION
.
387
13.7
COMMUNICATION
CHANNEL
AND
INFORMATION
PROCESSING
.
389
13.7.1
SEMANTIC,
SYNTACTIC
AND
PRAGMATIC
INFORMATION
.
390
13.7.2
INFORMATION,
FIRST-TIME
OCCURRENCE,
CONFIRMATION
.
391
13.8
SHANNON
'
S
BOUND
.
391
13.9
EXAMPLE
OF
THE
CHANNEL
CAPACITY
.
396
14
'
DETERMINISTIC
'
AND
STOCHASTIC
INFORMATION
.
399
14.1
INFORMATION
IN
STATE
SPACE
MODELS
.
399
14.2
THE
OBSERVATION
EQUATION
.
401
14.3
TRANSMISSION
FASTER
THAN
LIGHT
.
412
14.4
INFORMATION
ABOUT
STATE
SPACE
VARIABLES
.
413
15
MAXIMUM
ENTROPY
ESTIMATION
.
433
15.1
THE
DIFFERENCE
BETWEEN
MAXIMUM
ENTROPY
AND
MINIMUM
VARIANCE
.435
15.2
THE
DIFFERENCE
FROM
BOOTSTRAP
OR
RESAMPLING
METHODS
.
436
15.3
A
MAXIMUM
ENTROPY
EXAMPLE
.
437
15.4
MAXIMUM
ENTROPY:
THE
METHOD
.
438
XVI
TABLE
OF
CONTENTS
15.4.1
MAXIMUM
SHANNON
ENTROPY
.
438
15.4.2
MINIMUM
KULLBACK-LEIBLER
DISTANCE
.
442
15.5
MAXIMUM
ENTROPY
AND
MINIMUM
DISCRIMINATION
INFORMATION
.
446
15.6
GENERATION
OF
GENERALIZED
ENTROPY
MEASURES
.
449
15.6.1
EXAMPLE:
GAUSSIAN
DISTRIBUTION
AND
SHANNON
'
S
INFORMATION
.
452
16
CONCLUDING
REMARKS
.
463
16.1
INFORMATION,
ENTROPY
AND
SELF-ORGANIZATION
.
463
16.2
COMPLEXITY
THEORY
.
466
16.3
DATA
REDUCTION
.
467
16.4
CRYPTOLOGY
.
468
16.5
CONCLUDING
CONSIDERATIONS
.
468
16.5.1
INFORMATION,
ENTROPY
AND
PROBABILITY
.
470
16.6
INFORMATION
.
472
APPENDIX
.
475
A.
1
INEQUALITY
FOR
KULLBACK
'
S
INFORMATION.
475
A.2
THE
LOG-SUM
INEQUALITY
.
476
A.3
GENERALIZED
ENTROPY,
DIVERGENCE
AND
DISTANCE
MEASURES
.
481
A.
3.1
ENTROPY
MEASURES
.
481
A.3.2
GENERALIZED
MEASURES
OF
DISTANCE
.
488
A.3.
3
GENERALIZED
MEASURES
OF
THE
DIRECTED
DIVERGENCE
.
490
A.3
.4
GENERALIZED
MEASURES
OF
DIVERGENCE
.
493
A.3.
4.1
INFORMATION
RADIUS
AND
THE
J-DIVERGENCE
.
493
A.3.
4.2
GENERALIZATION
OF
THE
R-DIVERGENCE
.
494
A.3.
4.3
GENERALIZATION
OF
THE
J-DIVERGENCE
.
498
A.4
A
SHORT
INTRODUCTION
TO
PROBABILITY
THEORY
.
500
A.4.
1
AXIOMATIC
DEFINITION
OF
PROBABILITY
.
501
A.4.
1.1
EVENTS,
ELEMENTARY
EVENTS,
SAMPLE
SPACE
.
501
A.4.
1.2
CLASSES
OF
SUBSETS,
FIELDS
.
502
A.4.
1.3
AXIOMATIC
DEFINITION
OF
PROBABILITY
ACCORDING
TO
KOLMOGOROV
.
505
PROBABILITY
SPACE
.
506
A.4.
1.4
RANDOM
VARIABLES
.
506
A.4.
1.5
PROBABILITY
DISTRIBUTION
.
507
A.4.
1.6
PROBABILITY
SPACE,
SAMPLE
SPACE,
REALIZATION
SPACE
.
508
A.4.
1.7
PROBABILITY
DISTRIBUTION
AND
DISTRIBUTION
DENSITY
FUNCTION.
508
A.4.1.8
PROBABILITY
DISTRIBUTION
DENSITY
FUNCTION
(PDF)
.
510
A.
5
THE
REGULARITY
CONDITIONS
.
513
A.6
STATE
SPACE
DESCRIPTION
.
516
BIBLIOGRAPHY
.
519
INDEX
.
545 |
| any_adam_object | 1 |
| author | Arndt, Christoph |
| author_facet | Arndt, Christoph |
| author_role | aut |
| author_sort | Arndt, Christoph |
| author_variant | c a ca |
| building | Verbundindex |
| bvnumber | BV013605535 |
| callnumber-first | Q - Science |
| callnumber-label | Q370 |
| callnumber-raw | Q370 |
| callnumber-search | Q370 |
| callnumber-sort | Q 3370 |
| callnumber-subject | Q - General Science |
| classification_rvk | SK 830 |
| ctrlnum | (OCoLC)248179456 (DE-599)BVBBV013605535 |
| dewey-full | 003.54 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003.54 |
| dewey-search | 003.54 |
| dewey-sort | 13.54 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV013605535 |
| illustrated | Illustrated |
| indexdate | 2024-08-19T00:11:27Z |
| institution | BVB |
| isbn | 3540416331 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009294393 |
| oclc_num | 248179456 |
| open_access_boolean | |
| owner | DE-703 DE-573 DE-29T DE-20 DE-861 DE-634 DE-11 |
| owner_facet | DE-703 DE-573 DE-29T DE-20 DE-861 DE-634 DE-11 |
| physical | XIX, 547 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| spelling | Arndt, Christoph Verfasser aut Information measures information and its description in science and engineering C. Arndt Berlin [.a.] Springer 2001 XIX, 547 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Informationsmaß - Informationstheorie Informationstheorie - Entropie Entropie (DE-588)4014894-4 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Informationsmaß (DE-588)4330787-5 gnd rswk-swf Entropie (DE-588)4014894-4 s Informationstheorie (DE-588)4026927-9 s DE-604 Informationsmaß (DE-588)4330787-5 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009294393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arndt, Christoph Information measures information and its description in science and engineering Informationsmaß - Informationstheorie Informationstheorie - Entropie Entropie (DE-588)4014894-4 gnd Informationstheorie (DE-588)4026927-9 gnd Informationsmaß (DE-588)4330787-5 gnd |
| subject_GND | (DE-588)4014894-4 (DE-588)4026927-9 (DE-588)4330787-5 |
| title | Information measures information and its description in science and engineering |
| title_auth | Information measures information and its description in science and engineering |
| title_exact_search | Information measures information and its description in science and engineering |
| title_full | Information measures information and its description in science and engineering C. Arndt |
| title_fullStr | Information measures information and its description in science and engineering C. Arndt |
| title_full_unstemmed | Information measures information and its description in science and engineering C. Arndt |
| title_short | Information measures |
| title_sort | information measures information and its description in science and engineering |
| title_sub | information and its description in science and engineering |
| topic | Informationsmaß - Informationstheorie Informationstheorie - Entropie Entropie (DE-588)4014894-4 gnd Informationstheorie (DE-588)4026927-9 gnd Informationsmaß (DE-588)4330787-5 gnd |
| topic_facet | Informationsmaß - Informationstheorie Informationstheorie - Entropie Entropie Informationstheorie Informationsmaß |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009294393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT arndtchristoph informationmeasuresinformationanditsdescriptioninscienceandengineering |