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Analysis

Real, Complex, and Functional Analysis
ZaidAlyafey
  • Sticky
Discussions on the convergence of integrals and series
Replies
23
Views
26K
DreamWeaver
DreamWeaver
Peter
The Set of Borel Sets ... Axler Pages 28-29 ... ...
Replies
1
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14
Opalg
Opalg
Peter
Smallest Sigma Algebra ... Axler, Example 2.28 ...
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5
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66
Peter
Peter
Peter
Sigma Algebras ... Axler Page 26 ...
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2
Views
32
Peter
Peter
Peter
Translation Invariance of Outer Measure ... Axler, Result 2.7 ...
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2
Views
45
Peter
Peter
Peter
Outer measure of an open interval ...
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7
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118
Peter
Peter
Peter
Lebesgue Outer Measure ... Carothers, Proposition 16.2 (i) ...
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0
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37
Peter
Peter
Peter
Lebesgue Outer Measure ... Carothers, Proposition 16.1 ...
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2
Views
53
Peter
Peter
Peter
Outer measure of a closed interval ... Axler, Result 2.14 ...
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2
Views
48
Peter
Peter
Peter
Outer measure ... Axler, Result 2.14 ... Another Question ...
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3
Views
59
GJA
G
Peter
Lebesgue Outer Measure ... Carothers, Proposition 16.1 ...
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0
Views
30
Peter
Peter
Peter
Outer Measure ... Axler, Result 2.5 ...
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4
Views
176
Peter
Peter
J
Finding the Unique Solution of a Polar System with Variable Radius?
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0
Views
80
Jiggerjaw
J
mathmari
Weierstrass function
2
Replies
38
Views
1K
Klaas van Aarsen
Klaas van Aarsen
Peter
Lebesgue Integration of Simple Functions ... Lindstrom, Lemma 7.4.6 ... ...
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4
Views
471
Peter
Peter
Peter
Measurable Functions ... Lindstrom, Proposition 7.3.7 ... ...
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8
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194
Opalg
Opalg
A
monotony of a function
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2
Views
319
Country Boy
C
evinda
Show existence of a,b
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11
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238
Klaas van Aarsen
Klaas van Aarsen
Peter
Open Sets in a Discrete Metric Space ... ...
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2
Views
185
Peter
Peter
Peter
Open Sets in R ... ... Willard, Example 2.7 (a) ... ...
Replies
3
Views
300
GJA
G
mathmari
Limits & properties
Replies
23
Views
1K
Klaas van Aarsen
Klaas van Aarsen
S
Need help
Replies
1
Views
495
Prove It
P
mathmari
[SOLVED] Show that the two functions are identical
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4
Views
428
mathmari
mathmari
A
Laplace Convolution
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1
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500
Prove It
P
S
hello i would like some help with laplace transforms.
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2
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580
Prove It
P
D
need help with evaluating H(t-8t)2cosh(t-8)
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2
Views
481
Prove It
P
Peter
Intermediate Value Theorem ...Silva, Theorem 4.2.1 ... ...
Replies
3
Views
1K
GJA
G
Peter
Intermediate Value Theorem ... Browder, Theorem 3.16 ... ...
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2
Views
915
Peter
Peter
Peter
Increasing Function and Discontinuities ... Browder, Proposition 3.14 ... ...
Replies
1
Views
817
Peter
Peter
Peter
Continuity of f^+ ... Browder Corollary 3.13
Replies
4
Views
522
HallsofIvy
H
Peter
Relatively Open Sets ... Stoll, Theorem 3.1.16 (a) ...
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6
Views
670
Peter
Peter
Peter
Composition of Two Continuous Functions ... Browder, Proposition 3.12 ... ...
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0
Views
368
Peter
Peter
Peter
Increasing Function on an Interval ... Browder, Proposition 3.7 ... ...
Replies
3
Views
402
GJA
G
Peter
Relatively Open Sets ... Another Queston Regarding Stoll, Theorem 3.1.16 (a) ...
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0
Views
166
Peter
Peter
Peter
Continuity of a Function ... Conway, Definition 1.7.1 ... ...
Replies
3
Views
407
Opalg
Opalg
Peter
Riemann Integration .. Existence Result ... Browder, Theorem 5.12 ...
Replies
0
Views
211
Peter
Peter
Peter
Limits of Functions ...Conway, Proposition 2.1.2 ... ...
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0
Views
193
Peter
Peter
Peter
The Riemann and Darboux Integrals ... Browder, Theorem 5.10 ... ...
Replies
1
Views
275
Peter
Peter
Peter
The Riemann Integral ... Conway, Proposition 3.1.4 ...
Replies
2
Views
421
Peter
Peter
Peter
Differentials and Jacobians ... Remarks After Browder Prposition 8.21 ...
Replies
1
Views
396
Peter
Peter
Peter
An Example on Differentials ... Browder Proposition 8.12 ...
Replies
2
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500
Peter
Peter
Peter
Differentials/Total Derivatives in R^n ... Browder, Proposition 8.12 ...
Replies
2
Views
416
Peter
Peter
Peter
The Chain Rule in n Dimensions ... Browder Theorem 8.15 - Another Question ...
Replies
1
Views
412
Peter
Peter
L
Partial fraction decomposition
Replies
2
Views
1K
BestMethod
B
Peter
Yet Further Help ... Differentiabilty & Maxima ... Browder, Proposition 8.14 ... ...
Replies
2
Views
424
Peter
Peter
Peter
Differentials in R^n ... Another Remark by Browder, Section 8.2 ... ...
Replies
2
Views
481
Peter
Peter
Peter
The Chain Rule in n Dimensions ... Browder Theorem 8.15
Replies
0
Views
339
Peter
Peter
Peter
Another Question ... Differentiabilty & Maxima ... Browder, Proposition 8.14 ... ...
Replies
0
Views
287
Peter
Peter
Peter
Differentiabilty and Continuity of Vector-Valued Functions ... Browder, Proposition 8.13 ... ...
Replies
2
Views
452
Peter
Peter
Peter
Differentiabilty & Maxima of Vector-Valued Functions ... Browder, Proposition 8.14 ... ...
Replies
2
Views
490
Peter
Peter
Peter
Differentials in R^n ... Remark by Brwder, Section 8.2 ... ...
Replies
7
Views
730
Peter
Peter
Peter
Operator Norm and Sequences ... Yet a Further Question ... Browder, Proposition 8.7 ...
Replies
4
Views
634
Peter
Peter
Peter
Operator Norm and Sequences ... Another Question ... Browder, Proposition 8.7 ...
Replies
4
Views
539
Peter
Peter
Peter
Operator Norm and Cauchy Sequence ... Browder, Proposition 8.7 ...
Replies
1
Views
356
Opalg
Opalg
Peter
Operator Norm and Distance Function ... Browder, Proposition 8.6 ...
Replies
2
Views
304
Peter
Peter
G
calculations with stepfunction(heaviside)
Replies
1
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410
Klaas van Aarsen
Klaas van Aarsen
Peter
Operator norm ... Field, Theorem 9.2.9 ...
Replies
2
Views
323
Peter
Peter
Peter
Operator norm --- Remarks by Browder After Lemma 8.4 ...
Replies
2
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376
steep
S
Peter
The "Operator Norm" for Linear Transfomations ... Browder, page 179, Section 8.1, Ch. 8 ... ...
Replies
5
Views
882
Peter
Peter
Peter
Operator Norm ... differences between Browder and Field ...
Replies
2
Views
347
Peter
Peter
mathmari
The metrices are topologically but not strongly equivalent
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10
Views
809
Klaas van Aarsen
Klaas van Aarsen
Peter
Could R^n be a field ...?
Replies
3
Views
446
Opalg
Opalg
mathmari
[SOLVED] Strong equivalence of metrices
Replies
4
Views
307
mathmari
mathmari
mathmari
Prove statements about metric
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8
Views
690
mathmari
mathmari
Peter
Cauchy-Riemann Conditions for Differentiability ... Mathews & Howell, Theorem 3.4 ... ...
Replies
0
Views
221
Peter
Peter
Peter
Proof that Arcsin x is continuous ...
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3
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467
Peter
Peter
Peter
Differentiation of the Complex Square Root Function ... ... Palka, Example 1.5, Chapter III
Replies
2
Views
370
Peter
Peter
Peter
Yet Another Question on the Complex Square Root Function ... Palka, Example 1.5, Chapter III
Replies
0
Views
298
Peter
Peter
Peter
Further Questions on Complex Square Root Function ... Palka, Example 1.5, Section 1.2, Chapter III
Replies
2
Views
223
Peter
Peter
Peter
Complex Derivatives ... Palka, Examples 1.1 and 1.2, Chapter III, Section 1.2 ...
Replies
2
Views
308
Peter
Peter
Peter
Diiferentiability of Functions of a Complex Variable ... Markushevich, Theorem 7.1 ... ...
Replies
4
Views
377
Peter
Peter
Peter
The Square and Square Root Functions of a Complex Variable ... Gamelin, Ch. 1, Section 4
Replies
3
Views
795
Opalg
Opalg
AutGuy98
Question for Intermediate Analysis (Please Help!)
Replies
1
Views
459
Evgeny.Makarov
E
mathmari
Show that there is no order relation on K
Replies
9
Views
700
Evgeny.Makarov
E
mathmari
Show that there exists a bijection
Replies
8
Views
701
Evgeny.Makarov
E
AutGuy98
Another Question, But This One is About Proving a Function is One-to-One (PLEASE HELP)
Replies
2
Views
531
HallsofIvy
H
Peter
Complex Derivative ... Remark in Apostol, Section 16.1 ... ...
Replies
2
Views
559
Peter
Peter
N
infinite dimentional subspace need not be closed
Replies
1
Views
429
topsquark
topsquark
AutGuy98
Proof of an Infimum Being Equal to the Negative Form of a Supremum (Please Help!)
Replies
2
Views
716
AutGuy98
AutGuy98
AutGuy98
Proof of the Equality of Supremums (Or Something Like That Anyway :) )
Replies
1
Views
379
castor28
castor28
AutGuy98
Infimum and Supremum of a Set (Need Help Finding Them!)
Replies
1
Views
342
Opalg
Opalg
Peter
Complex Variable ... Differentiability Implies Continuity ... Conway and Mathews and Howell ... ...
Replies
2
Views
605
Peter
Peter
Peter
Upper and Lower Linits (lim sup and lim inf) - Denlinger, Theorem2.9.6 (b) ...
Replies
4
Views
935
Peter
Peter
Peter
Another Question on Upper and Lower Limits ... Denlinger, Theorem 2.9.6 (a)
Replies
2
Views
434
Peter
Peter
Peter
Upper and Lower Linits (lim sup and lim inf) - Sohrab Proposition 2.2.39 (a) ...
Replies
6
Views
548
Peter
Peter
Peter
Upper and Lower Linits (lim sup and lim inf) - Sohrab Proposition 2.2.39 (b) ...
Replies
2
Views
370
Peter
Peter
Peter
Compact Metric Spaces and Inverse Functions ... Apostol, Example After Theorem 4.29 ...
Replies
2
Views
532
Peter
Peter
Peter
Functions Continuous on Comapct Sets ... Apostol, Theorem 4.25 ...
Replies
2
Views
494
Peter
Peter
Peter
Limits of Complex Functions ... Zill & Shanahan, Theorem 3.1.1/ A1
Replies
3
Views
631
Peter
Peter
Peter
The Metric Space R^n and Sequences ... Remark by Carothers, page 47 ...
Replies
6
Views
821
Peter
Peter
Peter
The Definition of a Neighborhood and the Definition of an Open Set ... Carothers, Chapters 3 & 4 ...
Replies
2
Views
594
Peter
Peter
Peter
The Discrete Topology and the Discrete Metric Space ... Stromberg, Example 3.10 (b) ...
Replies
2
Views
531
Peter
Peter
Peter
Open Balls in a Normed Vector Space ... Carothers, Exercise 32
Replies
4
Views
727
Peter
Peter
Peter
Neighbourhoods and Open Neighbourhoods ... Browder, Proposition 6.8 ... ...
Replies
3
Views
569
Peter
Peter
Peter
Baire Category Theorem ... Stromberg, Theorem 3.55 ... ...
Replies
7
Views
829
Peter
Peter
Peter
Boundary of a Set in a Topological Space ... Browder, Remarks Following Defn 6.10, pages 125-126 ...
Replies
2
Views
520
Peter
Peter
Peter
Connectedness and Intervals in R ... Another Question ... Stromberg, Theorem 3.47 ... ...
Replies
2
Views
507
Peter
Peter
Peter
Connectedness and Intervals in R ... Stromberg, Theorem 3.47 ... ...
Replies
1
Views
554
HallsofIvy
H
Peter
Equivalent Statements to Compactness ... Another Question ... Stromberg, Theorem 3.43 ... ...
Replies
1
Views
405
Opalg
Opalg
Peter
Equivalent Statements to COmpactness ... Stromberg, Theorem 3.43 ... ...
Replies
2
Views
520
Peter
Peter
S
Maximum likelihood estimation
Replies
5
Views
595
SheepLon
S
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