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P. V. Reichelderfer On bounded variation and absolute continuity for parametric representations of continuous surfaces, Trans. Amer. Math. Soc. vol. 53 (1943) pp. 251-291. MR 0007917 (4:213e)

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J. Schauder Über stetige Abbildungen, Fund. Math. vol. 12 (1928) pp. 47-74.