A 1 ∪A 2 ∪…∪A n |=|A 1 |+|A 2 |+…+|A n
... n-permutation of S will also be called a permutation of S. For example, if S={2•a,1•b,3•c}, then aacb acbc cacc are 4-permutations of S, “abccac” is a permutation of S. The multiset S has no 7-permutations since 7>2+1+3=6, the number of objects of S. ...
... n-permutation of S will also be called a permutation of S. For example, if S={2•a,1•b,3•c}, then aacb acbc cacc are 4-permutations of S, “abccac” is a permutation of S. The multiset S has no 7-permutations since 7>2+1+3=6, the number of objects of S. ...
A new proof of Alexeyev`s Theorem
... In [1], Alexeyev has proved that whenever U is a unitary operator of the Hilbert space L2 (X, B, µ) with (X, B, µ) being a standard probability Borel space then there exists a bounded function f ∈ L∞ (X, B, µ) whose spectral measure realizes the maximal spectral type of U . The proof in [1] uses spe ...
... In [1], Alexeyev has proved that whenever U is a unitary operator of the Hilbert space L2 (X, B, µ) with (X, B, µ) being a standard probability Borel space then there exists a bounded function f ∈ L∞ (X, B, µ) whose spectral measure realizes the maximal spectral type of U . The proof in [1] uses spe ...
