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The notation $\|P\| \to 0$ means that the size of the largest subrectangle in the partition approaches zero. As the largest rectangle shrinks to zero area, all other rectangles in the partition must also shrink to zero.

Conditions: Applies to the limit step in the definition of volume by double Riemann sums.; $P$ represents the partition of the rectangular region.

The notation $\|P\| \to 0$ means that the size of the largest subrectangle in the partition approaches zero. As the largest rectangle shrinks to zero area, all other rectangles in the partition must also shrink to zero.

Conditions: Applies to the limit step in the definition of volume by double Riemann sums.; $P$ represents the partition of the rectangular region.

The infinitesimal base area $\Delta A_k = \Delta x_k \Delta y_k$ represents the footprint or base of a single representative rectangular box in the Riemann sum. It is the area of the $k$-th subrectangle in the domain partition.

Conditions: The domain is partitioned into subrectangles.; $\Delta x_k$ and $\Delta y_k$ are the side lengths of the $k$-th subrectangle.

The infinitesimal base area $\Delta A_k = \Delta x_k \Delta y_k$ represents the footprint or base of a single representative rectangular box in the Riemann sum. It is the area of the $k$-th subrectangle in the domain partition.

Conditions: The domain is partitioned into subrectangles.; $\Delta x_k$ and $\Delta y_k$ are the side lengths of the $k$-th subrectangle.