There is no infinite-dimensional Lebesgue measure

The Lebesgue measure is a way to measure size or length of a certain type of shape. However, the Lebesgue measure can only measure up to a certain number of dimensions. An infinite-dimensional shape or space is one that has an infinite number of dimensions. It is impossible to measure something that has an infinite number of dimensions because we are limited to measuring with a certain number of dimensions. So, the Lebesgue measure can only measure shapes that have a limited number of dimensions, not an infinite number.