Dirac Approximate Identity
See why a concentrating unit mass converges weakly while ordinary pointwise intuition fails.
Free theory articleSee why a concentrating unit mass converges weakly while ordinary pointwise intuition fails.
Concept & interpretation
The Dirac delta function is not an ordinary function but a measure or distribution. We can approximate it with a family of functions, called an approximate identity.
Experiment
Explore the approximate identity in the interactive module.
- Select Width epsilon to see the density concentrate and observe Peak density become Unbounded as epsilon approaches 0.
- Select Probe x to see the Point density decrease away from the origin.
- Select Closed window radius to see how the total mass is affected.
- Select Cosine frequency to see how the test integral is affected.