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The plateau of Arcadia, with basins at elevations of 1,650 to 3,300 feet (500 to 1,000 m), is bounded on the north by the Erímanthos and Killíni mountains and is itself divided by numerous subsidiary ranges.

Thus ( u m ) is bounded.

M is bounded and weak sequentially closed.

Consequently, (tau_{A,C}(M)) is bounded.

We assert that M is bounded.

It suffices to show that ( u m ) is bounded.

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Then for (p>1), (mathcal{M}) is bounded from (L^{p,lambda}) to (L^{p,lambda}) and for (p=1), (mathcal{M}) is bounded from (L^{1,lambda}) to (WL^{1,lambda}).

Then for (p>1), (mathcal{M}) is bounded from (widetilde{L}^{p,lambda}) to (widetilde{L}^{p,lambda}) and for (p=1), (mathcal{M}) is bounded from (widetilde{L}^{1,lambda}) to (Wwidetilde{L}^{1,lambda}).

This shows that ({mathcal {M}}) is bounded.

Since f n is an L q -Caratheodory function, { x m } is bounded in C 1 [ 0, 1 ], and { c D β x m } is bounded in C [ 0, 1 ].

If {t m } is bounded, we can use the above estimate and (2.18) to get c 0, 0 ≤ lim inf m → ∞ c λ m, δ m.

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