Chapter 14Distributions of Distributions

This chapter is dedicated to the space image′(Ω1; image′(Ω2; E)) of distributions on Ω1 with values in the space image′(Ω2; E) of distributions on Ω2.

  1. — We characterize these distributions, their bounded sets and their convergent sequences (§ 14.1 to 14.3).
  2. — We characterize the sets in which every bounded sequence has a convergent subsequence (§ 14.4). In particular, we show that every bounded sequence in image′(Ω1; image′(Ω2)) has a convergent subsequence.
  3. — We give conditions for a bounded sequence in image′ (Ω1; image′ (Ω2; E)) to have a converging subsequence in image′(Ω1; image′(Ω2; F )) ...

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