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funksional analiz misol va masalalar yechish 1 qism
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B & ! B ⊂ [A] A & B & [A] = R A & R * A & (x 0 −ε, x 0 + ε) ! A & ! ! & & ! ! ! & ! [ ' & ! (: 7, ( + + 7, + X ∗ " .& x, y, z ∈ X (x ∗ y) ∗ z = x ∗ (y ∗ z) ' /& e ∈ X x ∈ X e ∗ x = x ∗ e = x ' 0& x ∈ X x −1 ∈ X x ∗ x −1 = e (X, ∗) ! X x, y x ∗ y = y ∗ x X 2 ! [a, b) ! − S S [a, a) = ∅ S & & ( [a, b), [c, d) ∈ S [a, b) ∩ [c, d) ∈ S %"# 3b#"! 5 ! [a, b) ∈ S, [a 1 , b 1 ) ∈ S, [a 1 , b 1 ) ⊂ [a, b) [a, b)\[a 1 , b 1 ) = [a, a 1 ) ∪ [b 1 , b ) 3b%"! 5 [a, a 1 ) [b 1 , b ) S \ S % b%" S ' ! S & " & S A = [0, 5) B = [1, 3) & ' " A ΔB = [0, 1) ∪ [3, 5) S \ S S = {A ⊂ R : A yo R\A to plamlardan biri chekli } σ − ' S & " A n = {n} ∈ S, ∞ n=1 A n / ∈ S. $ * S & && bb" ( + - #5 A, B, C ∈ S ! (AB)C = A(BC) ( (A ∗ B) ∗ C = A ∗ (B ∗ C) %5 x ∈ X ! e ∗ x = x ∗ e = x " ! e ∈ X ∅ ∈ S , ∅A = A ∅ = A `5 + x = A ∈ S ! x −1 A ∈ S x ∗ x −1 = e A A = ∅ b5 x ∗ y = y ∗ x A B = BA () * +, * *+- + # - % * S & S ! & & * S & & ' * S & & . * S & & / * S & & A & ! ! & A(A)− E = A A & ! ! ! & " ' ! A ! & A & ! A ∅ & {A, ∅} E = A 2 ! ! & $ {P α } ! P = ∩ α P α % S & ! S " ! S ! ! P ! M(S) + & [0, 1) ! [a, b) ! ! , ' b#8" . b#8" σ − " / S A & A 1 , A 2 , . . . , A n & A & , A 1 , A 2 , . . . , A n & A n +1 , . . . , A s ∈ S & A & ! S ! A 1 , A 2 , . . . , A n &" ! S ! B 1 , . . . , B t & + A k & B 1 , . . . , B t & ( A k = ∪ s ∈M k B s ' M k ⊂ {1, 2, . . . , t} * S A k & ! A = ∪ k ≥1 A k , A k ∈ S ! A & X " 1 ! & c _ \ & c $ 2 ! ! & & 3 5 c % 2 ! ! ! ! & c & S = {A ⊂ R : A yo R\A to plamlardan biri chekli } " ' S = {A ⊂ R : A yo R\A to plamlardan biri chekli yoki sanoqli } " σ − . S = {A ∩ B : A ⊂ R − yopiq, B ⊂ R ochiq to plam } " / %$" σ − 2 S P A = {a, b, c} & ! ! & ! 2 ! ! & 3 5 c 2 ! [a, b] [a, b), (a, b] " (a, b) ' $ 1 ! ! {(x, y) : a < x ≤ b, c < y ≤ d} ! ' & % 1 (x, y) ∈ R 2 : a ≤ x < b, c ≤ y < d ! ! ' " + c ' c & S = {(x, y) : a ≤ x < b, c ≤ y < d} A 1 ⊂ A ! A = [0, 7) × [0, 7) A 1 = [1, 3) × [3, 5) & A \A 1 & ! ! ! A \A 1 & " ! & ' 2 ! ! & " ' σ − c σ − ! c . P A ∈ P ! P A {A ∩ B, B ∈ P} , & P A " * P σ − P A & σ − / X ! & , ! ! & σ − X & < & " c 1 5 {[a, b] : a ∈ Q, b ∈ Q ∧ a < b} ∪ ∅, 5 {(a, b] : a ∈ Z, b ∈ Z ∧ a < b} ∪ ∅, !5 {[a, b) : a ∈ R\Q, b ∈ R\Q ∧ a < b} ∪ ∅. X (& ! (& &" A(X) ”Δ” && $ § # * ' & ! (; . ! ' ! " X / ( σ − \ & / ( ! ( X / ( ! & $7, ! S μ μ : S μ → R + A 1 , A 2 , . . . , A n ∈ S μ n ∪ k =1 A k ∈ S μ μ n k =1 A k = n k =1 μ (A k ) μ : S μ → R + '! μ & #5 %5 ; `5 $" ∅ = ∅∪∅ μ (∅) = 2μ(∅), ( μ (∅) = 0 ! $7, ! m S m μ S μ (S m ⊂ S μ ) A ∈ S m μ (A) = m(A) |
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