In the book "Functional analysis and Semi-Groups" by E Hille and R S Phillips, theorem 7.4.1 states that subadditive functions defined on some interval $I$ and finite everywhere are bounded over compact sets $I^*\subset I$.
The proof in this book is kind of rough and I have been trying to make another proof - more elegant and/or with a different approach but I get nothing. I would appreciate any reference of another proof or another proof itself. Thank you.
2026-03-26 09:49:33.1774518573
On subadditive functions everywhere finite bounded on compact sets
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