违法事实 发表于 2025-3-26 23:15:09
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Locally Convex SpacesWe have seen in the preceding chapters the usefulness of weak convergence. From a theoretical point of view, it would be more satisfying to find a norm associated with weak convergence. In finite dimensions every norm is suitable because the weak and strong convergences are the same. In infinite dimensions the situation is quite different.扩大 发表于 2025-3-28 00:21:49
Monotone Functions. (having more than one point).不再流行 发表于 2025-3-28 04:40:28
The Lebesgue Integral in ,In former times when one invented a new function it was for a practical purpose; today one invents them purposely to show up defects in the reasoning of our fathers and one will deduce from them only that.—H. Poincaré谄媚于人 发表于 2025-3-28 06:58:50
Generalized Newton–Leibniz FormulaOne of the (if not .) most important theorems of classical analysis is the Newton–Leibniz formula: . allowing us to compute many integrals. The purpose of this chapter is to extend its validity to Lebesgue integrable functions.针叶 发表于 2025-3-28 13:18:01
Integrals on Measure SpacesIn Chap. 5 we defined the Lebesgue integral of functions defined on .. In this chapter we show that the theory remains valid in a much more general framework;moreover, almost all proofs can be repeated word for word. The results of this chapter include integrals of several variables and integrals on probability spaces