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Page 140
It can also be extended by defining the measure differently on the basic field E.
We shall illustrate this latter remark by describing here the construction of a
Radon measure on an interval. 15 Definition. An interval is a set of points in the ...
It can also be extended by defining the measure differently on the basic field E.
We shall illustrate this latter remark by describing here the construction of a
Radon measure on an interval. 15 Definition. An interval is a set of points in the ...
Page 141
The argument may be repeated by defining e3 — an>— c and choosing
appropriate points in the interval (c, 0+63]- By induction, it is clear that for every
integer k = 1, 2, . . ., there are points at, bt with c < a„ ^ 6n ^ . . . iŁ ax ^ 6X ^ c+ex
such that 2 ...
The argument may be repeated by defining e3 — an>— c and choosing
appropriate points in the interval (c, 0+63]- By induction, it is clear that for every
integer k = 1, 2, . . ., there are points at, bt with c < a„ ^ 6n ^ . . . iŁ ax ^ 6X ^ c+ex
such that 2 ...
Page 223
5 Let Abea function of bounded variation on the interval (a, b) and continuous on
the right. Let g be a function defined on (a, b) such that the Lebesgue-Stieltjes
integral / = jlg(s)dh(s) exists. Let / be a continuous increasing function on an open
...
5 Let Abea function of bounded variation on the interval (a, b) and continuous on
the right. Let g be a function defined on (a, b) such that the Lebesgue-Stieltjes
integral / = jlg(s)dh(s) exists. Let / be a continuous increasing function on an open
...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries 84 | 34 |
Copyright | |
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Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero