Principles of Mathematical Analysis |
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Page 28
... neighborhood of a point p is a set N , ( p ) consisting of all points q such that d ( p , q ) < r . The number r is called the radius of N , ( p ) . ( b ) A point p is a limit point of the set E if every neighborhood of p contains a ...
... neighborhood of a point p is a set N , ( p ) consisting of all points q such that d ( p , q ) < r . The number r is called the radius of N , ( p ) . ( b ) A point p is a limit point of the set E if every neighborhood of p contains a ...
Page 36
... neighborhoods , as follows . 1 1 Suppose P is We shall con- Let Vibe any neighborhood of x1 . If V1 consists of all y & R * such that yx1r , the corresponding closed neighborhood V1 is defined to be the set of all y ε R * such that ❘y ...
... neighborhoods , as follows . 1 1 Suppose P is We shall con- Let Vibe any neighborhood of x1 . If V1 consists of all y & R * such that yx1r , the corresponding closed neighborhood V1 is defined to be the set of all y ε R * such that ❘y ...
Page 85
... neighborhood of - - ∞ . 4.33 . Definition . Let f be defined on E. We say that f ( t ) → A as t → X , where A and x are in the extended real number system , if for every neighborhood U of A there is a neighborhood V of x such that ...
... neighborhood of - - ∞ . 4.33 . Definition . Let f be defined on E. We say that f ( t ) → A as t → X , where A and x are in the extended real number system , if for every neighborhood U of A there is a neighborhood V of x such that ...
Contents
Preface V | 1 |
ELEMENTS OF SET THEORY | 21 |
NUMERICAL SEQUENCES AND SERIES | 41 |
Copyright | |
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a₁ B₂ bounded variation C'-mapping called Cauchy sequence choose complex numbers continuous function continuous on a,b converges uniformly Corollary countable set Definition denote diverges Example Exercise exists f is differentiable finite fn(x follows Fourier series function defined function f ƒ and g ƒ ɛ ƒ is continuous given Hence Hint holds implies inequality integer integral interval k-form Lebesgue Lebesgue integral Let f lim inf lim sup limit point linear measurable functions metric space monotonic functions neighborhood nonnegative notation number system obtain open set P₁ partial sums partition polynomials positive integer properties Prove rational numbers real function real numbers Riemann integral say that f shows Suppose f Theorem uniform convergence uniformly continuous upper number variation on a,b vector space y₁