Category:Real Analysis Theorems
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Pages in category "Real Analysis Theorems"
The following 26 pages are in this category, out of 26 total.
1
UTLOC:1
A
A monotonically increasing sequence bounded above converges
Axiom of completeness
Axiom of completeness/Statement
C
Cauchy criterion for convergence
Cauchy-Schwarz inequality
Cauchy-Schwarz inequality for inner product spaces
Comparison test for real series
Comparison test for real series/Statement
E
Epsilon form of inequalities
Every convergent sequence is Cauchy
Every lingering sequence has a convergent subsequence
Every sequence in a compact space is a lingering sequence
G
Geometric series
Given a Hilbert space and a non-empty, closed and convex subset then for each point in the space there is a closest point in the subset
Greater than or equal to/Epsilon form
I
If a real series converges then its terms tend to zero
If a subsequence of a Cauchy sequence converges then the Cauchy sequence itself also converges
I cont.
If an inner product is non-zero then both arguments are non-zero
Intermediate value theorem
M
Mean value theorem
Monotonicity of the integral of non-negative extended-real-valued measurable functions with respect to a measure
O
Operations on convergent sequences of real numbers
T
The norm of a space is a uniformly continuous map with respect to the topology it induces
Triangle inequality
W
Weierstrass approximation theorem
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Theorems
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