1. ! "
# ! <
$ % & !
' & ! [ ]# $#"""#( ) *
=<<<= """) "
% $#"""#( )=σ $+#"""+#+(+ )=σ & ! [ ]# #
* +σ * σ * { } { }+#"""+#+#"""# )) ⊂
% $#"""#( )=σ $+#"""+#+(+ )=σ & ! * *
[ ]# # * , & * & ! * +σ *
σ & { } { }+#"""+#+#"""# )) ∪ "
-$ .
' * [ ]# [ ]#
& ! $#"""#( )=σ [ ]# * * !
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/ & ! σ & "
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& # & ! * σ & "
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& "
0 [ ]# # & !
& ! σ +σ # & ! ++σ * σ +σ
& " * & #
* # [ ]# # & ! & ++σ "
1 # * & [ ]# (*
[ ]# # $ 2&
3 2& [ ]# ( ! $"
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2. $
% [ ]# # $#"""#( )=σ & ! &
" 4 # [ ]# # ! ! !
] [#− " ! &
=
−−= $($#( σ
& ! σ & "
' & * +σ σ , #
$#($+#( σσ = "
1 # & , * +σ
* σ # $#($+#( σσ = "
0 # # & ! ++σ * +σ σ #
$#($++#($+#( σσσ == "
' [ ]# ! $#( σ #
& ! σ & "
[ ]#
" # !
[ ]
=
−−=
#
$( "
! 5 * 6
& * & "
' * * [ ]#
$( − 7 ! "
' *
! ( [ ]# # λ µ $
3 ! )≥ [ ]# #
[ ]
)
#
≥
3 /
[ ] [ ] [ ]
+=+
###
µλµλ
3 ! % << #
[ ] [ ] [ ]
+=
###
( ! *
& [ ]# [ ]# $"
3 % ≤ [ ]# #
[ ] [ ]
≤
##
(
! $
% [ ]# # * & " '
"
% $(−
ε & ϕ [ ]# * ( + 3 3
* ≤ϕ $
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3. 8
% $(+
ε & ψ [ ]# * ( + 3 3
* ψ≤ $
/ & $(−
ε $(+
ε ! $(−
ε
# $(+
ε "
% $(−
& $(−
ε "
% $(+
& $(+
ε "
/ & $(−
$(+
& ! #
$(−
$(+
# ϕ ψ
[ ]# * ψϕ ≤≤ # ψϕ ≤
#
[ ] [ ]
≤
##
ψϕ "
1 $(−
& # $(−
# $(+
& #
$(+
" # $($( +−
≤ "
% & # * & [ ]# #
[ ]# ! & "
1 # & [ ]# # * &
[ ]# "
& & 9 "
' * # # & &
[ ]# # * : !
( # ! * # *
# $(−
ε $(+
ε ; $
0 # & [ ]# # [ ]#
[ ]#
#
$( ( 2 # ! & #
* $"
' ! * & ! 5 * 6
& * & "
$ 1
% [ ]# " ' *
[ ]# & ! $#"""#( )=σ [ ]# *
* # ! ! ] [#− #
− "
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' ! * [ ]# # & ! σ
& # & ! * σ & "
* [ ]#
* & (! ; $# *
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4. <
(
$"
% [ ]# # $#"""#( )
& ! & " # * [ ]# #
! ! ] [#− &
[ ]#− "
* [ ]# &
# ! # * [ ]# #
[ ]#− # & "
& # & [ ]# # ,
[ ] [ ] [ ]− ###
)
)
#"""##$(#"""$(#$(
' # * &
[ ]#
[ ]# " 1 # * [ ]#
2& 3 2& [ ]# "
-$ 0
2
% [ ]# " #
ε # ϕ [ ]# * εϕ ≤− "
1
• = 7 [ ]# "
% )>ε
[ ]# ( 2 > $#
)>α *
[ ] [ ] ( )εα <−<−∈∀∈∀ $+($(+##+##
' 2 * α<
−
# & !
2 $#"""#( )=σ [ ]#
[ ] +=∈∀ ##) # !
−
= ( & ! 2 σ $
' 2 ϕ
[ ] [ [ $($(#### −− =∈∀∈∀ ϕ $($( =ϕ "
εϕ ≤−
% [ ]#∈
3 % = # εϕ ≤=− )$($(
3 % # [ ]#∈ * [ [#−∈ "
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5. ?
εϕ <−=− − $($($($( # 2 ! * #
[ [#−∈ # α<−≤− −−
• % *
' & ! $#"""#( )=σ & # # *
[ ]# # 2 $# *
[ ]#− * : ! ] [#− " 0 )>ε # *
* # *
[ ]#− ϕ * [ ] εϕ ≤−∈∀ − $($(## " '
ϕ [ ]#
[ ] $($(##) =∈∀ ϕ # [ ] ] [ $($(#### ϕϕ =∈∀∈∀ − "
ϕ ! [ ]# # εϕ ≤− "
2 #
2 (! $
% [ ]# " #
ε # ϕ ψ [ ]# *
ψϕ ≤≤ εϕψ ≤−
/ ! @ # ϕ
* εϕ ≤− # εϕϕ −=+ εϕψ +=+
++ ψϕ ≤≤ εϕψ ≤− # ! # ψϕ ≤≤ εϕψ ≤− #
! εϕ ≤− "
$ * &
2
[ ]# & [ ]# "
1
% [ ]# "
% )>ε " % 2 #
ϕ ψ [ ]# * ψϕ ≤≤ εϕψ ≤− "
# # $(−
∈εϕ $(+
∈εψ #
[ ] [ ]
≤≤≤ +−
##
$($( ψϕ "
#
[ ] [ ] [ ] [ ]
εεψϕψϕ $(
####
−=≤−=−
1 ε$($($() −≤−≤ −+
! & * * )>ε # #
# * )$($( =− −+
# # & [ ]# "
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6. ' * [ ]# * #
ε # ϕ ψ [ ]# *
ψϕ ≤≤ εϕψ ≤− "
& # *
& " 0 # * * 2
5 [ ]# 6# #
2 # ! * 2 5 [ ]#
& 6"
'
& & "
A *
• 0 & & "
% * [ ]#) ( + 3 3 $( = ∈ # ) $
% ϕ [ ]#) ≤ϕ # ! ] [#−
& ! & ϕ # ! ϕ
) * ! ) ] [#− (* $" 1
)$( =−
" 1 @ # $( =+
# 7 & ( 9 $"
• 0 # @ # &
% [ ]#) $( = )≠ # ) " 1 ,#
* )" 1 # !
ϕ ψ [ ]#) * ψϕ ≤≤ ≤−ϕψ " 0 #
! 3 ! [ ]α#) ! ) ≤< α # ϕ ψ
! [ ]#) & ! & ϕ ψ #
! "
# ε * ) << ε " [ ]#ε #
& # ! # ϕ ψ [ ]#ε #
ε " % ϕ ψ [ ]#) $( −=ϕ $( =ψ [ [ε#)∈ #
* ϕ ψ [ ]#) # * ψϕ ≤≤ # *
[ ] [ ] [ ] [ ]
εεεεϕψϕψϕψ
εε
8$(
##)#)#)
≤−+≤−+−=−
1 7# 2 )$($( =− −+
"
• 0 # * "
% [ ]#)
[ ]
$( = )≠ # ) "
#
( { })B∈ $" # * ε 2
(! * C ( * ε< $#
[ ]#) ) # ! ] ]# $
# # & " ( −=
π
$"
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