Generally, as long as the area where you slipped or tripped and fell is part of the property owner's property, and the property owner failed to fulfill a legal duty to take precautions to protect you from injuring yourself, the property owner will be legally responsible for your injuries.

Stairs
Stairs are often made of materials that become worn with continued use. Stair edges can become rounded and may cause people to slip when they step on them. A property owner will be liable for a slip and fall accident occurring on stairs, when the property owner knew of the dangerous condition, or the condition existed for sufficient time that the owner should have known about it. If the owner knew or should have known about a stairway condition, liability may arise when:   One or more steps are worn and rounded; Debris, such as trash, pieces of paper, dirt, gum, etc., is present on the stairs; The stairs have been waxed or polished, and the stair materials lack a non-skid surface; A handrail is missing or broken.

Escalators and Elevators
Common mechanisms for getting from one floor to another in a building are escalators and elevators. Because escalators and elevators are designed to carry passengers, in some instances, property owners have a higher legal duty than in other premises liability situations. When vehicles such as trains and buses are used for public transit, the owners of those vehicles are often held to a high standard of conduct. Some courts impose the same high standard of safety on owners and operators of escalators and elevators.

Slip and fall accidents can occur on escalators and elevators when there are unexpected, sudden movements or "jerks" in the machinery, or when articles of clothing, footwear, fingers, hands, or feet are caught in various parts of an escalator or elevator. Property owners are responsible for maintaining their escalators and elevators so that they operate safely.