Linear Operators: General theory |
From inside the book
Results 1-3 of 84
Page 106
... measurable , the function f is said to be μ - measurable or , if u is understood , simply measurable . A set A is measurable if % A is measurable . Symbols for the set of measurable functions are M ( S , E , μ , X ) , M ( S , Σ , μ ) ...
... measurable , the function f is said to be μ - measurable or , if u is understood , simply measurable . A set A is measurable if % A is measurable . Symbols for the set of measurable functions are M ( S , E , μ , X ) , M ( S , Σ , μ ) ...
Page 179
... measurable function defined on S and Let ¿ ( E ) = √2 f ( s ) u ( ds ) , E ΕΕΣ . g be a non - negative 2 - measurable function defined on S. Then fg is u - measurable , and E √2g ( s ) 2 ( ds ) = √¿¡ ( s ) g ( s ) μ ( ds ) , ΕΕΣ ...
... measurable function defined on S and Let ¿ ( E ) = √2 f ( s ) u ( ds ) , E ΕΕΣ . g be a non - negative 2 - measurable function defined on S. Then fg is u - measurable , and E √2g ( s ) 2 ( ds ) = √¿¡ ( s ) g ( s ) μ ( ds ) , ΕΕΣ ...
Page 180
... measurable function is the difference of two non- negative measurable functions , it follows from the theorem that [ * ] √g ( s ) λ ( ds ) = √1 ( 8 ) g ( s ) μ ( ds ) , E ΕΕΣ , for a real measurable function g . Since the real and ...
... measurable function is the difference of two non- negative measurable functions , it follows from the theorem that [ * ] √g ( s ) λ ( ds ) = √1 ( 8 ) g ( s ) μ ( ds ) , E ΕΕΣ , for a real measurable function g . Since the real and ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ