Cancellation of addition on convex sets

functional-analysis convex-analysis banach-spaces

Modulo result presented in this question the solution is extremely simple $$ A+C_0=B+C_0\Longleftrightarrow (A+C_0\subset B+C_0)\wedge(B+C_0\subset A+C_0)\Longrightarrow $$ $$ (A\subset B)\wedge (B\subset A)\Longleftrightarrow A=B $$

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