Various integration theories

Could anyone briefly explain, or point me towards a resource explaining, the main differences between the main integration theories, namely:

• Riemann Integration
• Riemann-Stieltjes Integration
• Lebesgue Integration
• Lebesgue-Stieltjes Integration

I understand that this a question with a potentially very long answer, since integration is no small theory. I can find information on these integrals separately, but I would really be interested in a comparison of these integrals with one another.

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Perhaps, you might be interested in this paper – Yuriy S Mar 24 at 7:22