Đặc trưng hóa sự thu gọn hình méo của không gian $$L_{p}$$ bằng các phép đo ngẫu nhiên

Armando W. Gutiérrez1
1Department of Mathematics and Systems Analysis, Aalto University, Otakaari 1, Espoo, Finland

Tóm tắt

Tóm tắt

Chúng tôi trình bày một đặc trưng hoàn chỉnh về sự thu gọn hình méo của không gian $$L_{p}$$Lp cho $$1\le p < \infty $$1p<. Mỗi thành phần của sự thu gọn hình méo của $$L_{p}$$Lp được thể hiện bằng một phép đo ngẫu nhiên trên một không gian Ba lan nhất định. Để minh họa, chúng tôi xem lại định lý ergodic trung bình $$L_{p}$$Lp cho $$1< p < \infty $$1<p< và ví dụ của Alspach về một phép đồng nhất trên một tập hợp lồi compact yếu trong $$L_{1}$$L1 mà không có điểm cố định.

Từ khóa


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