While it is forbidden to carry in a public area that has no eiruv on Shabbat, clearly a person can wear clothing without concern for this prohibition. The explanation for this is that clothing become batel (=nullified) with respect to the person who is wearing the clothing.
On yesterday’s daf we learned:
Rava said: If one carried out a living baby to the public domain on Shabbat, and a purse was hanging around the baby’s neck, he is liable for carrying out the purse.
The Gemara asks: And let him be liable for carrying out the baby as well.
The Gemara responds: Rava holds in accordance with the opinion of Rabbi Natan, who said: A living being carries itself. Therefore, one who carries a living being from one domain to another is not liable.
The Gemara asks: And let the purse be negated relative to the baby; and he should be exempt for carrying out the purse as well. Didn’t we learn in a Mishna: One who carries out a living person on a bed is exempt even for carrying out the bed, because the bed is secondary to the person? The same should be said with regard to the purse, relative to the baby.
The Gemara answers: In a case where a bed is relative to a living being, the living being negates it, as the bed is needed to carry the person and is secondary to him. However, in a case where a purse is relative to a baby, the baby does not negate it, since it is independently significant.
On today’s daf the Gemara applies this reasoning to cases of wearing clothing:
It was taught in a baraita in accordance with the opinion of Rava: On Shabbat, one who carries out his clothes to the public domain while they are folded and placed on his shoulder, and his sandals on his feet and his rings in his hand, not on his fingers, is liable. And if he was wearing them, he is exempt for all of them, as they are negated relative to him. One who carries out a person with his garments on him, and his sandals on his feet, and his rings on the fingers of his hands, i.e., wearing all of his clothes and jewelry in the typical manner, is exempt, whereas if he carried them out as they are, i.e., the person was holding his clothes in his hands, he is liable for carrying out the clothes, just as Rava said.