See Exercise 3.5 in "The geometry of fractal sets" by K. J. Falconer.

It says that any such set is an image of rectifiable curve.

For a short proof, check "Rectifiable curve" in my collection.

See Exercise 3.5 in "The geometry of fractal sets" by K. J. Falconer.

It says that any such set is an image of rectifiable curve.

For a short proof, check "Rectifiable curve" in my collection.

P.S. The earliest reference I found: Theorem 2 in Continua of finite linear measure. I. by Eilenberg and Harrold (1943).

See Exercise 3.5 in "The geometry of fractal sets" by K. J. Falconer.

It says that any such set is an image of rectifiable curve.

See Exercise 3.5 in "The geometry of fractal sets" by K. J. Falconer.

It says that any such set is an image of rectifiable curve.

For a short proof, check "Rectifiable curve" in my collection.