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15 Oct 2021: 24. 2.1.1 Examples of pseudo-Riemannian manifolds. 262.1.2 Causal geometry for Lorentzian manifolds.

15 Oct 2021: Theorem B.24. Let A = (a1,b1] (an,bn] be a rectangle in Rn, and supposef : A R is bounded.

15 Oct 2021: Chapter 4. The Fourier Transform and Sobolev Spaces. 4.1 The Fourier transform on L1(Rn). The Fourier transform is an extremely powerful tool across the full range of mathematics.Loosely speaking, the idea is to consider a function on Rn as a

15 Oct 2021: 24 Chapter 2 Distributions. 2.2 Derivatives of distributions. Things are looking good for Property ii) because the dual space to a vector space isnaturally a vector space.

21 Nov 2021: 2 =. 11. 1 dx =nj=1. Aj. 24. (iii) We have 11f(x) dx.

21 Nov 2021: as n. 24. 10 Distance and compact sets. This section could come almost anywhere in the notes, but provides somehelpful background to the section on Runge’s theorem.

15 Oct 2021: 24 Chapter 1 Lebesgue Integration Theory. The final of Littlewood’s principles is given flesh by.

8 Oct 2021: 24. and hecne X|fn(x)|pdµ(x). (sup. ‖g‖Lp′1. Xf(x)g(x)dµ(x). )p. If the rhs is finite, the monotone convergence Theorem applied to the