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Theorems in analysis
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131
1. Convergence tests
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Theorems in analysis
14
1.1. Abel's test
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Convergence tests
1.2. Alternating series test
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Convergence tests
1.3. Cauchy's convergence test
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Convergence tests
1.4. Cauchy's limit theorem
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Convergence tests
1.5. Cauchy condensation test
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Convergence tests
1.6. Dini test
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Convergence tests
1.7. Direct comparison test
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Convergence tests
1.8. Dirichlet's test
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Convergence tests
1.9. Integral test for convergence
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Convergence tests
1.10. Limit comparison test
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Convergence tests
1.11. Nth-term test
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Convergence tests
1.12. Ratio test
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Convergence tests
1.13. Root test
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Convergence tests
1.14. Stolz–Cesàro theorem
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Convergence tests
2. Fixed-point theorems
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Theorems in analysis
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2.1. Atiyah–Bott fixed-point theorem
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Fixed-point theorems
2.2. Bekić's theorem
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Fixed-point theorems
2.3. Borel fixed-point theorem
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Fixed-point theorems
2.4. Brouwer fixed-point theorem
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Fixed-point theorems
2.5. Browder fixed-point theorem
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Fixed-point theorems
2.6. Earle–Hamilton fixed-point theorem
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Fixed-point theorems
2.7. Fixed-point theorem
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Fixed-point theorems
2.8. Fixed-point theorems in infinite-dimensional spaces
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Fixed-point theorems
2.9. Kleene fixed-point theorem
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Fixed-point theorems
2.10. Lefschetz fixed-point theorem
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Fixed-point theorems
2.11. Markov–Kakutani fixed-point theorem
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Fixed-point theorems
2.12. Nielsen theory
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Fixed-point theorems
2.13. Ryll-Nardzewski fixed-point theorem
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Fixed-point theorems
2.14. Schauder fixed-point theorem
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Fixed-point theorems
2.15. Single-crossing condition
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Fixed-point theorems
3. Lemmas in analysis
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Theorems in analysis
17
3.1. Auerbach's lemma
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Lemmas in analysis
3.2. Bramble–Hilbert lemma
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Lemmas in analysis
3.3. Calderón–Zygmund lemma
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Lemmas in analysis
3.4. Closed and exact differential forms
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Lemmas in analysis
3.5. Céa's lemma
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Lemmas in analysis
3.6. Estimation lemma
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Lemmas in analysis
3.7. Grönwall's inequality
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Lemmas in analysis
3.8. Jordan's lemma
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Lemmas in analysis
3.9. Lebesgue's lemma
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Lemmas in analysis
3.10. Lions–Magenes lemma
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Lemmas in analysis
3.11. Mazur's lemma
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Lemmas in analysis
3.12. Poincaré lemma
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Lemmas in analysis
3.13. Schwarz lemma
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Lemmas in analysis
3.14. Spijker's lemma
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Lemmas in analysis
3.15. Stewart–Walker lemma
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Lemmas in analysis
3.16. Weyl's lemma (Laplace equation)
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Lemmas in analysis
3.17. Wiener's lemma
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Lemmas in analysis
4. Theorems in analytic number theory
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Theorems in analysis
16
4.1. Barban–Davenport–Halberstam theorem
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Theorems in analytic number theory
4.2. Brun–Titchmarsh theorem
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Theorems in analytic number theory
4.3. Chen's theorem
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Theorems in analytic number theory
4.4. Friedlander–Iwaniec theorem
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Theorems in analytic number theory
4.5. Hardy–Ramanujan theorem
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Theorems in analytic number theory
4.6. Kronecker limit formula
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Theorems in analytic number theory
4.7. Landau prime ideal theorem
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Theorems in analytic number theory
4.8. Landsberg–Schaar relation
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Theorems in analytic number theory
4.9. Linnik's theorem
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Theorems in analytic number theory
4.10. Maier's theorem
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Theorems in analytic number theory
4.11. Petersson trace formula
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Theorems in analytic number theory
4.12. Prime number theorem
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Theorems in analytic number theory
4.13. Ramanujan's master theorem
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Theorems in analytic number theory
4.14. Riemann–von Mangoldt formula
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Theorems in analytic number theory
4.15. Siegel–Walfisz theorem
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Theorems in analytic number theory
4.16. Vinogradov's mean-value theorem
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Theorems in analytic number theory
5. Theorems in approximation theory
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Theorems in analysis
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5.1. Arakelyan's theorem
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Theorems in approximation theory
5.2. Erdős–Turán inequality
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Theorems in approximation theory
5.3. Fejér's theorem
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Theorems in approximation theory
5.4. Lethargy theorem
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Theorems in approximation theory
5.5. Mergelyan's theorem
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Theorems in approximation theory
5.6. Walsh–Lebesgue theorem
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Theorems in approximation theory
5.7. Wirtinger's representation and projection theorem
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Theorems in approximation theory
6. ATS theorem
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Theorems in analysis
7. Ahlfors finiteness theorem
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Theorems in analysis
8. Ahlfors measure conjecture
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Theorems in analysis
9. Atkinson–Mingarelli theorem
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Theorems in analysis
10. Babuška–Lax–Milgram theorem
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Theorems in analysis
11. Besicovitch covering theorem
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Theorems in analysis
12. Brezis–Gallouët inequality
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Theorems in analysis
13. Carathéodory's existence theorem
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Theorems in analysis
14. Cartan–Kuranishi prolongation theorem
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Theorems in analysis
15. Cartan–Kähler theorem
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Theorems in analysis
16. Cauchy formula for repeated integration
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Theorems in analysis
17. Cauchy–Kovalevskaya theorem
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Theorems in analysis
18. Chebyshev–Markov–Stieltjes inequalities
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Theorems in analysis
19. Danskin's theorem
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Theorems in analysis
20. Denjoy–Koksma inequality
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Theorems in analysis
21. Denjoy–Young–Saks theorem
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Theorems in analysis
22. Dirichlet–Jordan test
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Theorems in analysis
23. Fenchel's duality theorem
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Theorems in analysis
24. Fenchel–Moreau theorem
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Theorems in analysis
25. Fraňková–Helly selection theorem
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Theorems in analysis
26. Fuchs' theorem
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Theorems in analysis
27. Gaussian integral
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Theorems in analysis
28. Glaeser's continuity theorem
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Theorems in analysis
29. Godunov's theorem
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Theorems in analysis
30. Goldbach–Euler theorem
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Theorems in analysis
31. Helly's selection theorem
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Theorems in analysis
32. Holmgren's uniqueness theorem
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Theorems in analysis
33. Integration using Euler's formula
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Theorems in analysis
34. Jensen's inequality
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Theorems in analysis
35. Kantorovich inequality
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Theorems in analysis
36. Khintchine inequality
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Theorems in analysis
37. Kneser's theorem (differential equations)
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Theorems in analysis
38. Komlós' theorem
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Theorems in analysis
39. Krein's condition
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Theorems in analysis
40. Lagrange reversion theorem
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Theorems in analysis
41. Malgrange preparation theorem
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Theorems in analysis
42. Malgrange–Ehrenpreis theorem
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Theorems in analysis
43. Malmquist's theorem
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Theorems in analysis
44. Markov brothers' inequality
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Theorems in analysis
45. Narasimhan–Seshadri theorem
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Theorems in analysis
46. Peano existence theorem
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Theorems in analysis
47. Picard–Lindelöf theorem
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Theorems in analysis
48. Poincaré inequality
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Theorems in analysis
49. Rademacher–Menchov theorem
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Theorems in analysis
50. Rellich–Kondrachov theorem
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Theorems in analysis
51. Remez inequality
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Theorems in analysis
52. Sard's theorem
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Theorems in analysis
53. Shift theorem
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Theorems in analysis
54. Silverman–Toeplitz theorem
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Theorems in analysis
55. Stahl's theorem
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Theorems in analysis
56. Stone–Weierstrass theorem
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Theorems in analysis
57. Sturm separation theorem
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Theorems in analysis
58. Sturm–Picone comparison theorem
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Theorems in analysis
59. Trudinger's theorem
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Theorems in analysis
60. Unique homomorphic extension theorem
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Theorems in analysis
61. Whitney extension theorem
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Theorems in analysis
62. Wirtinger's inequality for functions
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Theorems in analysis
Ancestors
Mathematical analysis
Fields of mathematics
Mathematics
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