Soit (E,A,μ) un espace mesure . On suppose qu′il existe un X∈A tel μ(X)=+∞ 1)Montrer que si μ est semi-finie alors ∀ r>0 il existe B⊆X tel que r<μ(B)< +∞


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Question Number 70980 by ~ À ® @ 237 ~ last updated on 10/Oct/19

$S o i t (E, A, μ) u n e s p a c e m e s u r e . O n s u p p o s e$ ${q u}^{'} i l e x i s t e u n X \in A t e l μ (X) = + \infty$ $1) M o n t r e r q u e s i μ e s t s e m i - f i n i e a l o r s$ $\forall r > 0 i l e x i s t e B \subseteq X t e l q u e r < μ (B) < + \infty$
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