Linear Operators, Part 2 |
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Page 113
... Borel set B” is replaced by “for each p-measurable set B." Although not all Carathéodory outer measures are Borel regular, the following theorems show that they do agree with Borel regular outer measures On the Borel sets. 4.57. THEOREM ...
... Borel set B” is replaced by “for each p-measurable set B." Although not all Carathéodory outer measures are Borel regular, the following theorems show that they do agree with Borel regular outer measures On the Borel sets. 4.57. THEOREM ...
Page 233
... Borel set E which separates them in the sense that PGE and QoE=0 (i.e., Qc X^ E). 2.34Ac Corollary (Souslin 1917). In a Polish space (X, d) if A is a set such that both A and its complement X- A are analytic then A is a Borel set. D ...
... Borel set E which separates them in the sense that PGE and QoE=0 (i.e., Qc X^ E). 2.34Ac Corollary (Souslin 1917). In a Polish space (X, d) if A is a set such that both A and its complement X- A are analytic then A is a Borel set. D ...
Page 824
... set with finite measure may be approximated by a finite union of disjoint open intervals . It must be noted that the union of these intervals in general neither contains nor is contained in the set which we ... Borel Sets Non-Measurable Sets.
... set with finite measure may be approximated by a finite union of disjoint open intervals . It must be noted that the union of these intervals in general neither contains nor is contained in the set which we ... Borel Sets Non-Measurable Sets.
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero