Linear Operators: General theory |
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Page 95
... function , complex function , etc. , where the adjectives real and complex refer to the range of the func- tion , the term set function is commonly used in ... DEFINITION . A set function u defined on a 95 Integration and Set Functions.
... function , complex function , etc. , where the adjectives real and complex refer to the range of the func- tion , the term set function is commonly used in ... DEFINITION . A set function u defined on a 95 Integration and Set Functions.
Page 182
... function ƒ of Theorems 2 and 7 is called the Radon - Nikodým derivative of λ with respect to μ and is often denoted by da / du . Thus d2 / du is defined ... function μ on Σ the equation μ ( 4 ̃1 ( E ) ) = μ2 ( E ) defines an additive set ...
... function ƒ of Theorems 2 and 7 is called the Radon - Nikodým derivative of λ with respect to μ and is often denoted by da / du . Thus d2 / du is defined ... function μ on Σ the equation μ ( 4 ̃1 ( E ) ) = μ2 ( E ) defines an additive set ...
Page 223
... function defined on ( a , b ) such that the Lebesgue - Stieltjes integral I = fag ( s ) dh ( s ) exists . Let ƒ be a continuous increasing function on an open interval ( c , d ) , with f ( c ) = a , f ( d ) b . Show that the Lebesgue ...
... function defined on ( a , b ) such that the Lebesgue - Stieltjes integral I = fag ( s ) dh ( s ) exists . Let ƒ be a continuous increasing function on an open interval ( c , d ) , with f ( c ) = a , f ( d ) b . Show that the Lebesgue ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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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