BY THE WAY (OF RANDOMNESS)
COMPLEXITY THROUGH
RANDOMNESS PART II
THE CONSPIRACY CONTINUES
BY THE WAY (OF RANDOMNESS)
THANKS TO:
PHILLIP POPP
JAVIER VILLEGAS
BY THE WAY (OF RANDOMNESS)
THE CANONICAL RANDOM VARIABLE [0, 1)
REVIEW: RANDOMNESS IS HARD
WE SEE
3D Scanning for Profile Acquisition and Reconstruction of Mayan Ceramics
Greg Shear June 2008
Cast and Background
Neighbor Jon Pagliaro works with Anabel Ford in UCSB's MesoAmerican Research Center Investigating variability in Late to Terminal Classic cer
3
Spaces Lp
1. Appearance of normed spaces. In this part we x a measure space
(, A, ) (we may assume that is complete), and consider the A measurable functions on it.
2. For f L1 (, ) set
f
1
=f
L1
=f
L1 (,)
|f | d.
=
It follows from the above inequalitie
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Measure theory II
1. Charges (signed measures). Let (, A) be a -algebra. A map
: A R is called a charge, (or signed measure or -additive set function) if
Aj =
j =1
( Aj )
(5.1)
j =1
for any disjoint countable family cfw_Aj , Aj A .
2. The equivalent
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Sequences of measurable functions
1. Let (, A, ) be a measure space (complete, after a possible application
of the completion theorem). In this chapter we investigate relations between various (nonequivalent) convergences of sequences of A -measurable
f
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Classical dualities and reexivity
1. Classical dualities. Let (, A, ) be a measure space. We will describe
the duals for the Banach spaces Lp () .
First, notice that any f Lp , 1 p , generates the linear functional
Ff on Lp by the rule
Ff (u) =
u Lp .
u