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To prove (P3), observe that (2) implies frac{1}{c}Tx+biggl 1-frac{1}{c}biggr)xin C frac{1}{c}Tx+biggl 1-frac{1}{c}biggr

Notice that for any,, so that (4.2) implies (4.7).

Furthermore, remark that (F3) implies (F 0,0,0,x) = 0) a.e. in (varOmega ).

We show that (H7) implies (H5) and (H6).

This also proves that (3) implies (4) and (4) implies (3).

First, we prove that (2.2) implies (2.3).

This shows that (4) implies (1).

Also, by noting that (CTheta=0), implies (C =0).

It is clear that (H10) implies (H3).

Finally, we show that (21) implies (16).

It is trivial that (1.7) implies (1.6).